Noteables Interactive Study Notebook - McGraw-Hill Higher Education

Contributing AuthorDinah Zike®ConsultantDouglas Fisher, Ph.D.Professor of Language and Literacy EducationSan Diego State UniversitySan Diego, CA

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may bereproduced or distributed in any form or by any means, or stored in a database or retrieval system, withoutthe prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storageor transmission, or broadcast for distance learning.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027Printed in the United States of America.ISBN: 978-0-07-890237-6 Math Connects: Concepts, Skills, and Problem Solving, Course 2MHID: 0-07-890237-1 Noteables: Interactive Study Notebook with Foldables ®1 2 3 4 5 6 7 8 9 10 009 17 16 15 14 13 12 11 10 09 08

ContentsFoldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . 21-1 A Plan for Problem Solving . . . . . . . . . . 41-2 Powers and Exponents . . . . . . . . . . . . . . 61-3 Squares and Square Roots . . . . . . . . . . . 81-4 Order of Operations . . . . . . . . . . . . . . . 101-5 Problem-Solving Investigation:Guess and Check . . . . . . . . . . . . . . . . . . 121-6 Algebra: Variables and Expressions . . . 131-7 Algebra: Equations . . . . . . . . . . . . . . . . 151-8 Algebra: Properties . . . . . . . . . . . . . . . . 181-9 Algebra: Arithmetic Sequences . . . . . . 201-10 Algebra: Equations and Functions . . . . 23Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . 774-1 Prime Factorization . . . . . . . . . . . . . . . 794-2 Greatest Common Factor . . . . . . . . . . . 814-3 Problem-Solving Investigation:Make an Organized List . . . . . . . . . . . . 844-4 Simplifying Fractions . . . . . . . . . . . . . . 854-5 Fractions and Decimals . . . . . . . . . . . . . 874-6 Fractions and Percents . . . . . . . . . . . . . 904-7 Percents and Decimals . . . . . . . . . . . . . 924-8 Least Common Multiple . . . . . . . . . . . . 944-9 Comparing and Ordering RationalNumbers . . . . . . . . . . . . . . . . . . . . . . . . 96Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . 322-1 Integers and Absolute Value . . . . . . . . 342-2 Comparing and Ordering Integers . . . 362-3 The Coordinate Plane . . . . . . . . . . . . . . 382-4 Adding Integers . . . . . . . . . . . . . . . . . . 412-5 Subtracting Integers . . . . . . . . . . . . . . . 442-6 Multiplying Integers . . . . . . . . . . . . . . . 462-7 Problem-Solving Investigation:Look for a Pattern . . . . . . . . . . . . . . . . 482-8 Dividing Integers . . . . . . . . . . . . . . . . . 49Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . 553-1 Writing Expressions and Equations . . . 573-2 Solving Addition and SubtractionEquations . . . . . . . . . . . . . . . . . . . . . . . 593-3 Solving Multiplication Equations . . . . . 613-4 Problem-Solving Investigation:Work Backward . . . . . . . . . . . . . . . . . . . 633-5 Solving Two-Step Equations . . . . . . . . . 643-6 Measurement: Perimeter and Area . . . 673-7 Functions and Graphs . . . . . . . . . . . . . . 69Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . 1035-1 Estimating with Fractions . . . . . . . . . . 1045-2 Adding and Subtracting Fractions . . . 1065-3 Adding and Subtracting MixedNumbers . . . . . . . . . . . . . . . . . . . . . . . 1085-4 Problem-Solving Investigation:Estimate Possibilities . . . . . . . . . . . . . 1105-5 Multiplying Fractions and MixedNumbers . . . . . . . . . . . . . . . . . . . . . . . 1115-6 Algebra: Solving Equations . . . . . . . . 1135-7 Dividing Fractions and MixedNumbers . . . . . . . . . . . . . . . . . . . . . . . 115Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 117Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . 1216-1 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 1236-2 Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 1256-3 Rate of Change and Slope . . . . . . . . . 1286-4 Measurement: Changing CustomaryUnits . . . . . . . . . . . . . . . . . . . . . . . . . . 1306-5 Measurement: Changing MetricUnits . . . . . . . . . . . . . . . . . . . . . . . . . . 1336-6 Algebra: Solving Proportions . . . . . . . 1366-7 Problem-Solving Investigation:Draw a Diagram . . . . . . . . . . . . . . . . . 1386-8 Scale Drawings . . . . . . . . . . . . . . . . . . 1396-9 Fractions, Decimals, and Percents . . . 142Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 144Math Connects, Course 2 iii

Organizing Your Foldables® Have students make this Foldable to help themorganize and store their chapter Foldables.Begin with one sheet of 11" × 17" paper.FoldFold the paper in half lengthwise. Then unfold.Fold and GlueFold the paper in half widthwise and glue all of the edges.Glue and LabelGlue the left, right, and bottom edges of the Foldableto the inside back cover of your Noteables notebook.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.FoldablesOrganizerReading and Taking Notes As you read and study each chapter, recordnotes in your chapter Foldable. Then store your chapter Foldables insidethis Foldable organizer.Math Connects, Course 2 v

Members who do not reside in the UK are not covered for third party and areadvised to obtain suitable cover before leaving their normal residence.Non UK residents should also ensure that any travel policy commences on the day theyleave their normal residence. It is unlikely that participants not resident in the UK will beable to obtain cover once they arrive in the UK. Overseas members who have beentouring the UK prior to taking part in a CTC tour should ensure that their existing travelpolicy is extended to cover the tour if necessary.Warning: Should you decide for whatever reason to delay the commencement of yourinsurance cover until nearer your departure date e.g. to start an annual policy, you riskthe loss of payments made before the policy comes into effect should it becomenecessary for you to cancel your booking.9. 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Thecompany shall not be liable for any damages caused by the total or partial failure to carry outthe contract if such failure is:i) attributable to the participant or any member of his or her party,ii)orthe fault of a third party unconnected to either the leader or the companyoriii) a result of unusual or unforeseen circumstances beyond the control of the leader, thecompany or the supplier of the service in question which could not have been predicted oravoided even after taking all reasonable care (see clause 18 Force majeure)iv)orthe fault of any person who was not carrying out work for us (generally or in particular)at the time.Where the company is found to be liable for damages in respect of its failure to carry out thecontract the maximum amount of such damages will be limited to the price paid for the tour.Where the damages relate to the provision of transport by air, sea or rail, or hotelaccommodation, any compensation payable will be further limited by the Warsaw Conventionas amended by the Hague Protocol 1955 (Air), the Athens Convention 1974 (Sea), the BerneConvention 1961 (Rail), the Paris Convention 1962 (Hotel Accommodation) and theInternational Convention for the Carriage of Passengers & Luggage by Road 1974. Flights orother transportation such as coach, ferry or rail journeys that form part of the package aresubject to the general conditions of carriage of the company concerned. Any independentarrangements made by the participant that are not part of the tour are entirely at his or herown risk.12. Cycles in transitIn the event of a cycle being lost, delayed or damaged on the outward journey, the companyshall not be responsible financially or otherwise for the inability of the participant to continuewith their holiday. The leader will endeavour to make alternative arrangements in suchcircumstances but this cannot be guaranteed.13. Joining the groupIf you are joining the holiday locally, our responsibility does not commence until the appointedtime at the designated meeting point. If you fail to arrive at the appointed time for whateverreason, we will not be responsible for any additional expenses incurred by you to meet upwith the group.14. Should you have a complaintIn the event of problems arising during the tour, participants should try to resolve themdirectly with the leader. If the problem cannot be resolved at this time an incident report formwill be completed by the leader, a copy of which will be given to you. On return to the UK youshould write to CTC Cycling Holidays & Tours Ltd, c/o 32 Hawthorn Walk, Newcastle uponTyne NE4 7HP, giving full details of any complaint and enclosing your copy of the incidentreport form. This letter must be received by the company within 21 days of your return.Complaints will be dealt with in accordance with the procedures of the company under whichthe complaint will be investigated by a senior official within a given timescale. Should anamicable solution not be agreed an appeal will be handled at Board level.If, despite our best efforts and having followed the above procedure for reporting andresolving your complaint, you feel that it has not been satisfactorily settled, we recommendthat it be referred for arbitration under the ABTOT Travel Industry Arbitration Service. Anindependent Arbitrator will review the documents relating to any complaint and deliver abinding decision to bring the matter to a close. Details of this scheme are available fromABTOT, Tower 42, Old Broad Street, London EC2N 1HQ. This scheme cannot decide incases where the sums claimed exceed £1500 per person or £7500 per booking form, or forclaims that are solely or mainly in respect of physical injury or illness or the consequencethereof.15. Special requestsAny special requests made on your booking form will be noted but, although we will do ourvery best to comply with these, we cannot guarantee they will be provided.16. Travel arrangementsAll timings are provisional and for your guidance only. Final details will be advised nearer thetime of departure.17. LeadersWe reserve the right to substitute leaders should circumstances make this necessary.18. Force majeureThis is the term applied to unusual and unforeseeable circumstances that are beyond ourcontrol. Compensation payments do not apply to changes, cancellations or curtailmentcaused by reason of war, threat of war, riots, civil strife, terrorist activities, industrial disputes,natural or nuclear disaster, fire, adverse weather conditions, floods etc, technical problems oftransport, closure or congestion at airports or ports, cancellation or changes of schedule byairlines or similar events. We cannot accept responsibility where the performance or promptperformance of our contract with you is prevented or affected as a result of suchcircumstances.19. 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®3–2 Solving Addition and Subtraction EquationsEXAMPLES Solve an Addition EquationMAIN IDEA Solve 14 + y = 20. Check your solution.• Solve addition and14 + y = 20 Write the equation.subtraction equations.14 from̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲each side. Simplify.=Lessons cover the contentof the lessons in your textbook.As your teacher discusses eachexample, follow along andcomplete the fill-in boxes. Takenotes as appropriate.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTSSubtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.Addition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.Write theseproperties in yourown words under theEquations tab.Check14 + y = 20 Write the original equation.14 + 20 Replace y with .The solution is .= 20 ̌ Simplify.Solve a + 7 = 6. Check your solution.a + 7 = 6 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲Checka + 7 = 6Foldables featurereminds you to takenotes in your Foldable.Subtract= Simplify.from each side.Write the original equation.+ 7 6 Replace a with .= 6 ̌ Simplify. The solution is.Check Your Progress Solve each equation.a. -6 = x + 4 b. m + 9 = 22Math Connects, Course 2 593–5EXAMPLEExamples parallel theexamples in the textbook.PARKS There are 76 thousand acres of state parkland inGeorgia. This is 4 thousand acres more than three timesthe number of acres of state parkland in Mississippi.How many acres of state parkland are there inMississippi?Words Three times the number of acres of stateparkland in Mississippi plus 4,000 is 76,000.VariableEquationLet m = the acres of state parkland inMississippi.Three times thenumber of acresof parklandin Mississippi plus 4,000 is 76,000.4,000 = 76,000+ 4,000 = 76,000 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲ Subtracteach side.= Simplify.fromCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.C H A P T E R3Use your Chapter 3 Foldableto help you study for yourchapter test.BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKER3-1Writing Expressions and EquationsTo make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go to:glencoe.comMatch the phrases with the algebraic expressions thatrepresent them.1. seven plus a number a. 7 - nb. 7 · n2. seven less a numberc. n - 73. seven divided by a numberd. n_ 7e. 7 + n4. seven less than a numberWrite each sentence as an algebraic equation.5. The product of 4 and 6. Twenty divided bya number is 12. y is equal to -10.3-2Solving Addition and Subtraction Equations7. Explain in words how to solve a - 10 = 3.Solve each equation. Check your solution.8. w + 23 = -11 9. 35 = z - 15BUILD YOURVOCABULARYYou can use your completedVocabulary Builder(pages 55–56) to help yousolve the puzzle.HOMEWORKASSIGNMENTPage(s):Exercises:66 Math Connects, Course 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.There are= Divide each side by .= Simplify.acres of state parkland in Mississippi.Check Your Progress BASEBALL Matthew had 64 hitsduring last year’s baseball season. This was 8 less than twicethe number of hits Gregory had. How many hits did Gregoryhave during last year’s baseball season?Check Your ProgressExercises allow you tosolve similar exerciseson your own.Bringing It All TogetherStudy Guide reviewsthe main ideas and keyconcepts from each lesson.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.72 Math Connects, Course 2Math Connects, Course 2 vii

NOTE-TAKING TIPSYour notes are a reminder of what you learned in class. Taking good notes canhelp you succeed in mathematics. The following tips will help you take betterclassroom notes.• Before class, ask what your teacher will be discussing in class. Reviewmentally what you already know about the concept.• Be an active listener. Focus on what your teacher is saying. Listen forimportant concepts. Pay attention to words, examples, and/or diagramsyour teacher emphasizes.• Write your notes as clear and concise as possible. The following symbolsand abbreviations may be helpful in your note-taking.Word or PhraseSymbol orAbbreviationWord or PhraseSymbol orAbbreviationfor example e.g. not equal ≠such as i.e. approximately ≈with w/ therefore ∴without w/o versus vsand + angle ∠• Use a symbol such as a star (★) or an asterisk (*) to emphasize importantconcepts. Place a question mark (?) next to anything that you do notunderstand.• Ask questions and participate in class discussion.• Draw and label pictures or diagrams to help clarify a concept.• When working out an example, write what you are doing to solve theproblem next to each step. Be sure to use your own words.• Review your notes as soon as possible after class. During this time, organizeand summarize new concepts and clarify misunderstandings.Note-Taking Don’ts• Don’t write every word. Concentrate on the main ideas and concepts.• Don’t use someone else’s notes as they may not make sense.• Don’t doodle. It distracts you from listening actively.• Don’t lose focus or you will become lost in your note-taking.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.viii Math Connects, Course 2

C H A P T E R1 Introduction to Algebra and FunctionsChapter 1®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with eleven sheets of notebook paper.Staple the eleven sheetstogether to form abooklet.Make each one 2 lineslonger than the onebefore it.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Write the chapter titleon the cover and labeleach tab with the lessonnumber.NOTE-TAKING TIP: When taking notes, it is oftena good idea to write a summary of the lesson inyour own words. Be sure to paraphrase key points.Math Connects, Course 2 1

C H A P T E R1BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 1.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplealgebraalgebraic expression[al-juh-BRAY-ihk]arithmetic sequence[air-ith-MEH-tik]basecoefficientdefining the variabledomainequation[ih-KWAY-zhuhn]equivalent expressionevaluateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.exponent2 Math Connects, Course 2

Chapter 1 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplefactorsfunctionfunction rulenumerical expressionorder of operationsperfect squarepowersCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.radical signrangesequencesolutionsquaresquare roottermvariableMath Connects, Course 2 3

1–1A Plan for Problem SolvingEXAMPLE Use the Four-Step PlanMAIN IDEA• Solve problems usingthe four-step plan.SPENDING A can of soda holds 12 fluid ounces. A 2-literbottle holds about 67 fluid ounces. If a pack of six canscosts the same as a 2-liter bottle, which is the betterbuy?UNDERSTAND What are you trying to find? You know thenumber of fluid ounces of soda in one can ofsoda. You need to know the number of fluidounces of soda in a pack of six cans.PLANYou can find the number of fluid ounces of sodain a pack of six cans bythenumber of fluid ounces in one can by .SOLVE 12 × =There arefluid ounces of soda in a packORGANIZE ITSummarize the four-stepproblem-solving plan onthe Lesson 1-1 page ofyour Foldable.®CHECKof six cans. The number of fluid ounces of sodain a 2-liter bottle is aboutthe. Therefore,is the better buybecause you get more soda for the same price.The answer makes sense based on the factsgiven in the problem.Check Your Progress FIELD TRIP The sixth-grade classat Meadow Middle School is taking a field trip to the local zoo.There will be 142 students plus 12 adults going on the trip. Ifeach school bus can hold 48 people, how many buses will beneeded for the field trip?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4 Math Connects, Course 2

1–1EXAMPLE Use a Strategy in the Four-Step PlanPOPULATION For every 100,000 people in the UnitedStates, there are 5,750 radios. For every 100,000 peoplein Canada, there are 323 radios. Suppose Sheamus livesin Des Moines, Iowa, and Alex lives in Windsor, Ontario.Both cities have about 200,000 residents. About howmany more radios are there in Sheamus’s city than inAlex’s city?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTSProblem-SolvingStrategies• guess and check• look for a pattern• make an organized list• draw a diagram• act it out• solve a simpler problem• use a graph• work backward• eliminate possibilities• estimate reasonableanswers• use logical reasoning• make a modelUNDERSTAND You know the approximate number of radiosper 100,000 people in both Sheamus’s city andAlex’s city.PLANYou can find the approximate number of radiosin each city bythe estimateper 100,000 people by two to get an estimateper 200,000 people. Then,find how many more radios there are in DesMoines than in Windsor.SOLVE Des Moines: 5,750 × 2 =CHECKWindsor: 323 × 2 =- =So, Des Moines has aboutmore radios than Windsor.Based on the information given in the problem,the answer seems to be reasonable.Check Your Progress READING Ben borrows a 500-pagebook from the library. On the first day, he reads 24 pages. Onthe second day, he reads 39 pages and on the third day he reads54 pages. If Ben follows the same pattern of number of pagesread for seven days, will he have finished the book at the endof the week?toMath Connects, Course 2 5

1–2 Powers and ExponentsMAIN IDEA• Use powers andexponents.BUILD YOUR VOCABULARY (pages 2–3)Two or more numbers that are multiplied together to formaare called factors.The exponent tells how many times the base is usedas a .The base is the common .Numbers expressed usingpowers.are calledFive to theFour to thepower is five squared.power is four cubed.ORGANIZE ITOn the Lesson 1-2 pageof your Foldable, explainthe difference betweenthe terms power andexponent.®EXAMPLES Write Powers as ProductsWrite each power as a product of the same factor.8 4Eight is used as a factor times. 8 4 =4 6is used as a factor six times. 4 6 =Check Your Progress Write each power as a product ofthe same factor.a. 3 6 b. 7 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6 Math Connects, Course 2

1–2BUILD YOUR VOCABULARY (pages 2–3)You can evaluate, or find theof,by multiplying the factors.Numbers writtenare instandard form.Numbers writtenare inexponential form.WRITE ITExplain how you woulduse a calculator toevaluate a power.EXAMPLES Write Powers in Standard FormEvaluate each expression.8 3 = =6 4 = =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress Evaluate each expression.a. 4 4 b. 5 5EXAMPLE Write Numbers in Exponential FormWrite 9 · 9 · 9 · 9 · 9 · 9 in exponential form.9 is the . It is used as a factor times.So, the exponent is .=Check Your Progress Write 3 · 3 · 3 · 3 · 3 inexponential form.Math Connects, Course 2 7

1–3 Squares and Square RootsMAIN IDEA• Find squares ofnumbers and squareroots of perfectsquares.BUILD YOUR VOCABULARY (pages 2–3)The of a number and is thesquare of the number.Perfect squares like 9, 16, and 225 are squares ofnumbers.Themultiplied to form perfect squares are calledsquare roots.A radical sign, √ , is the symbol used to indicate thepositiveof a number.EXAMPLES Find Squares of Numbers®ORGANIZE ITOn the Lesson 1-3 pageof your Foldable, explainin words and symbolshow you find squaresof numbers and squareroots of perfect squares. Find the square of 5.Multiply 5 by . · = 25 Find the square of 19.METHOD 1 Use paper and pencil.· =METHOD 2 Use a calculator.x 2 ENTERCheck Your Progress Find the square of each number.a. 7 b. 21Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8 Math Connects, Course 2

1–3KEY CONCEPTSquare Root A squareroot of a number is oneof its two equal factors.EXAMPLES Find Square RootsFind √ 36 .What number times itself is 36?· = 36, so √ 36 = .Find √ 676 .Use a calculator.2nd x 2 ENTERSo, √ 676 = .Check Your Progress Find each square root.a. √ 64 b. √ 529Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:GAMES A checkerboard is a square with an area of1,225 square centimeters. What are the dimensions ofthe checkerboard?The checkerboard is a square. By finding the square root of thearea, 1,225, you find the length of one side.2nd x 2 ENTER Use a calculator.The dimensions of the checkerboard are cm by cm.Check Your Progress GARDENING Kyle is planting anew garden that is a square with an area of 42.25 square feet.What are the dimensions of Kyle’s garden?2nd x 2 ENTERMath Connects, Course 2 9

1–4 Order of OperationsMAIN IDEA• Evaluate expressionsusing the order ofoperations.BUILD YOUR VOCABULARY (pages 2–3)The expressions 4 · 6 - (5 + 7) and 8 · (9 - 3) + 4 areexpressions.Order of operations arethat ensure thatnumerical expressions have only one value.KEY CONCEPTOrder of Operations1. Evaluate theexpressions insidegrouping symbols.2. Evaluate all powers.3. Multiply and dividein order from leftto right.4. Add and subtractin order from leftto right.®Be sure toinclude the order ofoperations on theLesson 1-4 page of yourFoldable.EXAMPLES Evaluate ExpressionsEvaluate each expression.27 - (18 + 2)27 - (18 + 2) = 27 - Add fi rst since 18 + 2 isin parentheses.15 + 5 · 3 - 2= Subtract 20 from 27.15 + 5 · 3 - 2 = 15 + - 2 Multiply 5 and 3.Check Your Progress= - 2 Add 15 and 15.= Subtract 2 from 30.Evaluate each expression.a. 45 - (26 + 3) b. 32 - 3 · 7 + 4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10 Math Connects, Course 2

1–4EXAMPLES Use Order of OperationsEvaluate each expression.12 × 3 - 2 212 × 3 - 2 2 = 12 × 3 - Find the value of 2 2 .= - 4 Multiply 12 and 3.= Subtract 4 from 36.REMEMBER ITIf an exponent liesoutside of groupingsymbols, complete theoperations within thegrouping symbols beforeapplying the power.28 ÷ (3 - 1) 228 ÷ (3 - 1) 2 = 28 ÷ Subtract 1 from 3 inside theparentheses.= 28 ÷ Find the value of 2 2 .= Divide.Check Your ProgressEvaluate each expression.a. 9 × 5 + 3 2 b. 36 ÷ (14 - 11) 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Evaluate an ExpressionMONEY Julian is buying one box of favors, one box ofballoons, and three rolls of crepe paper. What is thetotal cost?Item Quantity Unit Costcrepe paper 3 rolls $2favors 1 box $7balloons 1 box $51 × 7 + 1 × 5 + 3 × 2 = 7 + + 6 or 18The total cost is .Check Your Progress What is the total cost of two boxesof favors, two boxes of balloons, and six rolls of crepe paper?Math Connects, Course 2 11

1–5 Problem-Solving Investigation:Guess and CheckEXAMPLE Use Guess and Check StrategyMAIN IDEA• Solve problems usingthe guess and checkstrategy.CONCESSIONS The concession stand at the school playsold lemonade for $0.50 and cookies for $0.25. They sold7 more lemonades than cookies, and they made a total of$39.50. How many lemonades and cookies were sold?UNDERSTAND You know the cost of each lemonade andcookie. You know the total amount madeand that they soldmore lemonadesthan cookies. You need to know how manylemonades and cookies were sold.PLANSOLVEMake a guess and check it. Adjust the guessuntil you get the correct answer.Make a guess.14 cookies, 21 lemonades 0.25 (14) + 0.50 (21)This guess is too . =HOMEWORKASSIGNMENTPage(s):Exercises:CHECK50 cookies, 57 lemonades 0.25 (50) + 0.50 (57)This guess is too . =48 cookies, 55 lemonades 0.25 (48) + 0.50 (55)48 cookies cost $12 and 55 lemonades cost$27.50. Since $12 + $27.50 = $39.50 and 55 is7 more than 48, the guess is correct.Check Your Progress ZOO A total of 122 adults andchildren went to the zoo. Adult tickets cost $6.50 and children’stickets cost $3.75. If the total cost of the tickets was $597.75,how many adults and children went to the zoo?=Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.12 Math Connects, Course 2

1–6 Algebra: Variables and ExpressionsMAIN IDEA• Evaluate simplealgebraic expressions.BUILD YOUR VOCABULARY (pages 2–3)You can use a, or variable, in an expression.The expression 7 + n is called anexpression.The branch of mathematics that involves expressionswithTheis called algebra.factor of a term that contains avariable is called a coefficient.EXAMPLES Evaluate ExpressionsEvaluate t - 4 if t = 6.t - 4 = 6 - Replace t with .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= Subtract.Evaluate 5x + 3y if x = 7 and y = 9.5x + 3y = 5 · + 3 · Replace x withand with 9.= + Do all multiplications fi rst.= Add and 27.Evaluate 5 + a 2 if a = 5.5 + a 2 = 5 + 5 2 Replace a with .= 5 + Evaluate the .= Add.Math Connects, Course 2 13

1–6®ORGANIZE ITRecord and evaluatean example of a simplealgebraic expression onthe Lesson 1-6 page ofyour Foldable.Check Your Progress Evaluate each expression.a. 7 + m if m = 4.b. 4a - 2b if a = 9 and b = 6.c. 24 - s 2 if s = 3.EXAMPLE Evaluate an ExpressionHOMEWORKASSIGNMENTPage(s):Exercises:TEMPERATURE The formula for rewriting a Fahrenheittemperature as a Celsius temperature is __ 5 (F - 32), where9F equals the temperature in degrees Fahrenheit. Findthe Celsius equivalent of 99°F.__ 5 (F - 32)9= __ 5 (99 - 32)9_= 5 (67)9= _ 3359Replace F with 99.Subtract from 99and multiply.≈ Divide 335 by 9.The Celsius equivalent of 99°F is about 37.2°C.Check Your Progress BOWLING David’s cost for bowlingcan be described by the formula 1.75 + 2.5g, where g is thenumber of games David bowls. Find the total cost of bowling ifDavid bowls 3 games.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14 Math Connects, Course 2

1–7Algebra: EquationsMAIN IDEA• Write and solveequations using mentalmath.BUILD YOUR VOCABULARY (pages 2–3)An equation is ain mathematics thatcontains an equals sign.The solution of an equation is a number that makesthe sentence .The process of finding ais calledsolving an equation.When you choose ato represent one of theunknowns in an equation, you are defining the variable.EXAMPLE Solve an Equation MentallyCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITOn the Lesson 1-7 pageof your Foldable, recordand solve an example ofan algebraic equations.®Solve p - 14 = 5 mentally.p - 14 = 5 Write the equation.- 14 = 5 You know that 19 -14 is .= 5 Simplify.The solution is .Check Your Progress Solve p - 6 = 11 mentally.Math Connects, Course 2 15

1–7EXAMPLETEST EXAMPLE A store sells pumpkins for $2 per pound.Paul has $18. Use the equation 2x = 18 to find how largea pumpkin Paul can buy with $18.A 6 lb B 7 lb C 8 lb D 9 lbRead the ItemSolvecan weigh.to find how many pounds the pumpkinSolve the ItemWrite the equation.2 · = 18 You know that 2 · 9 is 18.Paul can buy a pumpkin as large aspounds.The answer is .Check Your Progress A store sells notebooks for $3 each.Stephanie has $15. Use the equation 3x = 15 to find how manynotebooks she can buy with $15.F 4 G 5 H 6 J 7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16 Math Connects, Course 2

1–7EXAMPLE Write an Equation to Solve a ProblemREVIEW ITExplain how to add adecimal and a wholenumber. (PrerequisiteSkill)ENTERTAINMENT An adult paid $18.50 for herself and twostudents to see a movie. If the two student tickets cost$11 together, what is the cost of the adult ticket?WordsVariableEquationThe cost of one adult ticket and two studenttickets is $18.50.Let a represent the cost of an adult movieticket.a + 11 = 18.50a + 11 = 18.50Write the equation.+ 11 = 18.50 Replace a with= 18.50 Simplify.to make the equation true.The numberis the solution of the equation. So, thecost of an adult movie ticket is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress ICE CREAM Julie spends $9.50 atthe ice cream parlor. She buys a hot fudge sundae for herselfand ice cream cones for each of the three friends who are withher. Find the cost of Julie’s sundae if the three ice cream conestogether cost $6.30.Math Connects, Course 2 17

1–8 Algebra: PropertiesMAIN IDEA• Use Commutative,Associative, Identity,and Distributiveproperties to solveproblems.BUILD YOUR VOCABULARY (pages 2–3)The expressions 5($9 + $2) and 5($9) + 5($2) are equivalentexpressions because they have thevalue.EXAMPLES Use the Distributive PropertyUse the Distributive Property to rewrite eachexpression. Then evaluate it.8 (5 + 7)8 (5 + 7) = 8 · + 8 ·KEY CONCEPTDistributive PropertyTo multiply a sum by anumber, multiply eachaddend of the sum bythe number outside theparentheses.6 (9) + 6 (2)= + Multiply.= Add.ORGANIZE ITOn the Lesson 1-8 pageyour Foldable, be sureto include examplesshowing the additionand multiplicationproperties.®6 (9) + 6 (2) = + Multiply.= Add.Check Your Progress Use the Distributive Property toevaluate each expression.a. 4 (6 + 3)b. (5 + 3) 7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.18 Math Connects, Course 2

1–8KEY CONCEPTSCommutative PropertyThe order in which twonumbers are added ormultiplied does notchange their sum orproduct.Associative PropertyThe way in which threenumbers are groupedwhen they are addedor multiplied does notchange their sum orproduct.Identity PropertyThe sum of an addendand zero is the addend.The product of a factorand one is the factor.EXAMPLEVACATIONS Mr. Harmon has budgeted $150 per day forhis hotel and meals during his vacation. If he plans tospend six days on vacation, how much will he spend?6 (150) = 6 (100 + ) 150 = 100 + 50.= (100) + (50) Distributive Property= 600 + or 900 Multiply, then add.Mr. Harmon will spend abouton a six-day vacation.Check Your Progress COOKIES Heidi sold cookies for$2.50 per box for a fundraiser. If she sold 60 boxes of cookies,how much money did she raise?BUILD YOUR VOCABULARY (pages 2–3)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Properties are statements that arenumbers.EXAMPLE Identify Propertiesfor allFind 5 · 13 · 20 mentally. Justify each step.5 · 13 · 20 = 5 · · Communtative Property ofMultiplication= ( · 20) · 13 Associative Property ofMultiplication= · 13 or Multiply 100 and 13Mentally.Check Your Progress Name the property shown by thestatement 4 + (6 + 2) = (4 + 6) + 2.Math Connects, Course 2 19

1–9 Algebra: Arithmetic SequencesMAIN IDEA• Describe therelationships andextend terms inarithmetic sequences.BUILD YOUR VOCABULARY (pages 2–3)A sequence is an list of .Each number in ais called a term.In an arithmetic sequence, each term is found bythe same number to theterm.EXAMPLES Describe Patterns in SequencesDescribe the relationship between the terms in eacharithmetic sequence. Then write the next three terms inthe sequence.ORGANIZE ITWrite an example ofan arithmetic and ageometric sequence onthe Lesson 1-9 page ofyour Foldable.®7, 11, 15, 19, …7, 11, 15, 19, ...+ + +Each term is found by4 to the previous term.Continue the pattern to find the next three terms.19 + 4 = 23 + 4 = 27 + 4 =The next three terms are 23, 27, and 31.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.20 Math Connects, Course 2

1–90.1, 0.5, 0.9, 1.3, …0.1, 0.5, 0.9, 1.3, …+ + +Each term is found by adding to the previous term.Continue the pattern to find the next three terms.1.3 + = 1.7 1.7 + = 2.1 + 0.4 =The next three terms are 1.7, 2.1, and 2.5.Check Your Progress Describe the relationshipbetween the terms in each arithmetic sequence. Thenwrite the next three terms in the sequence.a. 13, 24, 35, 46, …b. 0.6, 1.5, 2.4, 3.3, …Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITIn your own words,explain how todetermine the patternin a sequence.EXAMPLE Use a TableEXERCISE Mehmet started a new exercise routine. Thefirst day, he did 2 sit-ups. Each day after that, he did 2more sit-ups than the previous day. If he continues thispattern, how many sit-ups will he do on the tenth day?Position Operation Value of Term1 22 2 · 23 · 2 6d d · 2 2d(continued on the next page)Math Connects, Course 2 21

1–9Each term is 2 times its position number. So, the expressionis .2nWrite the expression.2 ( ) = 20 Replace n with 10.So, on the tenth day, Mehmet will dosit-ups.Check Your Progress CONCERTS The first row of atheater has 8 seats. Each additional row has eight more seatsthan the previous row. If this pattern continues, what algebraicexpression can be used to find the number of seats in the 15 throw? How many seats will be in the 15 th row?HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.22 Math Connects, Course 2

1–10 Algebra: Equations and FunctionsMAIN IDEA• Make function tablesand write equations.BUILD YOUR VOCABULARY (pages 2–3)A relationship where one thing depends on another iscalled a function.Theperformed on the input is given bythe function rule.REMEMBER ITWhen x and y areused in an equation,x usually representsthe input and y usuallyrepresents the output.You can organize thenumbers,numbers, and the function rule in a function table.The set ofvalues is called the domain.The set ofvalues is called the range.EXAMPLE Make a Function TableCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Asha earns $6.00 an hour working at a grocery store.Make a function table that shows Asha’s total earningsfor working 1, 2, 3, and 4 hours.Input Function OutputNumber ofHoursMultiply by 6TotalEarnings ($)1 62 6 × 246 × 3 18Math Connects, Course 2 23

1–10Check Your Progress MOVIE RENTAL Dave goes to thevideo store to rent a movie. The cost per movie is $3.50. Makea function table that shows the amount Dave would pay forrenting 1, 2, 3, and 4 movies.EXAMPLESREADING Melanie read 14 pages of a detective noveleach hour. Write an equation using two variables toshow how many pages p she read in h hours.Input Function OutputNumber ofHours (h)Multiply by 14Number ofPages Read (p)1 1 × 142 28hWordsVariable3 × 14 42numberof pages equalsread14hpagesLet p represent the number of pages read.Lettimesrepresent the number of hours.numberof hoursCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Equationp =24 Math Connects, Course 2

1–10READING Use your equation from Example 2 to find howmany pages Melanie read in 7 hours.Write the equation.p = 14 ( ) Replace h with 7.p =Multiply.Melanie read 98 pages in 7 hours.Check Your Progressa. TRAVEL Derrick drove 55 miles per hour to visit hisgrandmother. Write an equation using two variables to showhow many miles m he drove in h hours.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:b. TRAVEL Use your equation from above to find how manymiles Derrick drove in 6 hours.Math Connects, Course 2 25

C H A P T E R1BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 1 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 1, go to:glencoe.comYou can use your completedVocabulary Builder(pages 2–3) to help yousolve the puzzle.1-1A Plan for Problem SolvingUnderline the correct term to complete each sentence.1. The (Plan, Solve) step is the step of the four-step plan in whichyou decide which strategy you will use to solve the problem.2. According to the four-step plan, if your answer is not correct, youshould (estimate the answer, make a new plan and start again).3. Once you solve a problem, make sure your solution contains anyappropriate (strategies, units or labels).1-2Powers and ExponentsIdentify the exponent in each expression.4. 5 8 5. 8 3Evaluate each expression.6. 4 3 7. 8 5Complete the sentence.8. Numbers written with exponents are inform, whereas numbers written without exponents are inform.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.26 Math Connects, Course 2

Chapter 1 BRINGING IT ALL TOGETHER1-3Squares and Square RootsComplete each sentence.9. The square of 3 means × .10. Nine units squared means 9 withofunit each.Find the square of each number.11. 16 12. 28Find the square root of each number.13. √ 121 14. √ 4841-4Order of OperationsEvaluate each expression.15. 9 + 18 ÷ 6 16. (7 - 4) 2 ÷ 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. 2 × 4 2 ÷ 4 - 1 18. 8 + 2 (9 - 5) - (2 · 3)1-5Problem-Solving Investigation: Guess and CheckSolve using the guess and check strategy.19. MONEY Gary deposited $38 into his savings account every weekfor eight weeks. At the end of this time, the total amount in hisaccount was $729. How much money did Gary have in his accountbefore the deposits?Math Connects, Course 2 27

Chapter 1 BRINGING IT ALL TOGETHER1-6Algebra: Variables and ExpressionsEvaluate each expression if a = 5 and b = 6.20. 2a + 3b21. _ ab522. a 2 - 3b1-7Algebra: EquationsSolve each equation mentally.23. 5 + b = 12 24. h - 6 = 325. 12 · 4 = n 26. 2 = x _427. 9t = 54 28. 35 ÷ c = 71-8Algebra: PropertiesMatch the statement with the property it shows.29. 5 + (3 + 6) = (5 + 3) + 6 a. DistributiveProperty30. 8 + 0 = 8 b. CommutativeProperty of Addition31. 4 (7 - 2) = 4 (7) - 4 (2) c. Associative Propertyof Addition32. 10 + 9 = 9 + 10 d. Identity Propertyof AdditionCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.28 Math Connects, Course 2

Chapter 1 BRINGING IT ALL TOGETHER1-9Algebra: Arithmetic SequencesComplete the sentence.33. In an arithmetic sequence, each term is found bythe same number to the previous term.34. In a geometric sequence, each term is found bythe same number by the previous term.What is the next term in each of the following sequences?35. 1, 5, 25, … 36. 7, 10, 13, …1-10Algebra: Equations and Functions37. Complete the function table. Identify the domain and range.Then graph the function.x 2x - 1 yy-1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.01Domain =Range =OxMath Connects, Course 2 29

C H A P T E R1ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 1.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 1 Practice Test onpage 75 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 1 Study Guide and Review onpages 70–74 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 1 Practice Test onpage 75 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 1 Foldables.• Then complete the Chapter 1 Study Guide and Review onpages 70–74 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 1 Practice Test onpage 75 of your textbook.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature30 Math Connects, Course 2

C H A P T E R2 Integers®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of 8 _ 1 " × 11" paper.2Fold one sheet in halffrom top to bottom.Cut along fold fromedges to margin.Chapter 2Fold the other sheetin half from top tobottom. Cut along foldbetween margins.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Insert first sheetthrough second sheetand align folds.Label each page witha lesson number and title.NOTE-TAKING TIPS: When you take notes, it ishelpful to list ways in which the subject matterrelates to daily life.Math Connects, Course 2 31

C H A P T E R2BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 2.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleabsolute valueadditive inversecoordinate planegraphinteger[IHN-tih-juhr]negative integeroppositesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.32 Math Connects, Course 2

Chapter 2 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleordered pairoriginpositive integerquadrantCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.x-axisx-coordinatey-axisy-coordinateMath Connects, Course 2 33

2–1 Integers and Absolute ValueMAIN IDEA• Read and writeintegers, and find theabsolute value of anumber.BUILD YOUR VOCABULARY (pages 32–33)An integer is any from the set {…, -4, , -2,-1, 0, 1, , 3, 4, …}.To graph aon the number line, draw a point onthe line at its .Negative integers are integersPositive integers are integersthan zero.than zero.®ORGANIZE ITUnder Lesson 2-1 in yournotes, draw a numberline and graph a fewpositive and negativeintegers. Then write afew real world situationsthat can be described bynegative numbers.EXAMPLES Write Integers for Real-Life SituationsWrite an integer for each situation.a total rainfall of 2 inches below normalBecause it represents below normal, the integer is .a seasonal snowfall of 3 inches above normalBecause it represents normal, the integer is .Check Your Progress Write an integer for eachsituation.a. a total snowfall of 5 inches above normalb. an average monthly temperature of 4 degrees below normalCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.34 Math Connects, Course 2

2–1BUILD YOUR VOCABULARY (pages 32–33)The numbersand 5 are the samefrom 0, so -5 and 5 have the same absolute value.EXAMPLE Graph IntegersGraph the set of integers {-1, 3, -2} on a number line.Draw a number line. Then draw aeach integer.at the location ofCheck Your Progress Graph the set of integers {-2, 1, -4}on a number line.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTAbsolute Value Theabsolute value of aninteger is the distancethe number is from zeroon a number line.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLES Evaluate ExpressionsEvaluate the expression ⎪-5⎥ .On the number line, the graph of -5 is 5 units from 0. So, ⎪-5⎥ = .Evaluate the expression ⎪-4⎥ - ⎪-3⎥ .⎪-4⎥ - ⎪-3⎥ = - ⎪-4⎥ = , ⎪-3⎥ == Subtract.Check Your ProgressEvaluate each expression.a. ⎪-9⎥ b. ⎪8⎥ - ⎪-5⎥Math Connects, Course 2 35

2–2 Comparing and Ordering IntegersEXAMPLE Compare IntegersMAIN IDEA• Compare and orderintegersReplace the with < or > to make -9 -5 a truesentence.Graph each integer on a number line. Since is to the of -5, -9 -5.Check Your Progress-3 -6 a true sentence.Replace the with < or > to makeEXAMPLE Order IntegersTEST EXAMPLE The lowest temperatures in Europe,Greenland, Oceania, and Antarctica are listed in thetable. Which list shows the temperatures in order fromcoolest to warmest?ContinentRecord LowTemperature (°F)Europe -67Greenland -87Oceania 14Antarctica -129Source: The World AlmanacA -67, -87, 14, -129 C -129, -87, -67, 14B 14, -67, -87, -129 D -67, -87, -129, 14Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.(continued on the next page)36 Math Connects, Course 2

2–2®ORGANIZE ITUnder Lesson 2-2 in yourFoldable, explain howto compare integers. Besure to include examples.Read the ItemTo order the integers, graph them on a number line.Solve the Item Order the integers from least to greatest by reading from leftto right. The order from least to greatest is , ,, . The answer is .Check Your Progress MULTIPLE CHOICE The lowesttemperatures on a given day in four cities in the UnitedStates are listed in the table. Which of the following lists thetemperatures in order from coolest to warmest?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:CityLow TemperaturePortland, OR -12New York City, NY -6Denver, CO 7Newport, RI -3F -3, -6, 7, 12 H -12, 7, -6, -3G -12, -6, -3, 7 J -3, -6, 7, -12Math Connects, Course 2 37

2–3EXAMPLES Identify QuadrantsGEOGRAPHY Use the map of Utah shown below.TremontonVernalCedarCityBluffIn which quadrant is Vernal located?Vernal is located in theright quadrant.Quadrant .Which of the cities labeled on the map of Utah is locatedin quadrant IV?Quadrant is the bottom right quadrant. So, isin Quadrant IV.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress Refer to the map of Utahshown above.a. In which quadrant is Tremonton located?b. Which of the cities labeled on the map of Utah shown aboveis located in Quadrant III?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.40 Math Connects, Course 2

2–4 Adding IntegersEXAMPLES Add Integers with the Same SignMAIN IDEA• Add integers.Find -6 + (-3).Use a number line.• Start at .• Move 6 units to show -6.• From there, move units left to show . So, -6 + (-3) = .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTSAdding Integers withthe Same Sign The sumof two positive integersis positive. The sum oftwo negative integers isnegative.Additive InverseProperty The sum of anynumber and its additiveinverse is 0.Find -34 + (-21) .-34 + (-21) = Both integers are negative, so thesum is .Check Your Progress Find each sum.a. -5 + (-2) b. -27 + (-19)BUILD YOUR VOCABULARY (pages 32–33)The integers 5 and -5 are called opposites of each otherbecause they are the same distance from 0, but onsides of 0.Two that are are also calledadditive inverses.Math Connects, Course 2 41

2–4KEY CONCEPTAdding Integers withDifferent Signs To addintegers with differentsigns, subtract theirabsolute values. Thesum is:• positive if the positiveinteger has the greaterabsolute value.• negative if the negativeinteger has the greaterabsolute value.EXAMPLES Add Integers with Different SignsFind 8 + (-7).Use a number line.Start at .Move units right.Then move units left. So, 8 + (-7) = .Find -5 + 4.Use a number line.Start at .®ORGANIZE ITSummarize the steps foradding integers. Be sureto include examples.Moveunits left.Then move 4 units . So, -5 + = -1Check Your Progress Add.a. 6 + (-2) b. -3 + 5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.42 Math Connects, Course 2

2–4EXAMPLES Add Integers with Different SignsFind 2 + (-7).2 + (-7) = Subtract absolute values;7 - 2 = 5. Since has thegreater absolute value, the sum is.Find -9 + 6.-9 + 6 = the absolute values;9 - 6 = 3. Since -9 has theREMEMBER ITCompare theabsolute value ofthe addends whendetermining the signof the sums.absolute value, thesum is negative.Check Your Progress Add.a. 5 + (-9) b. 7 + (-3)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Use the Additive Inverse PropertyFind 11 + (-4) + (-11).11 + (-4) + (-11) = 11 + (-11) + (-4) CommutativeProperty (+)= + (-4) Additive InverseProperty= -4 Identity Property(+)Check Your Progress Find 5 + (-11) + (-5) .Math Connects, Course 2 43

2–5EXAMPLE Evaluate an ExpressionALGEBRA Evaluate g - h if g = -2 and h = -7.g - h = - Replace with -2 andh with .= -2 + Subtract -7, add .= Simplify.Check Your Progress Evaluate m - n if m = -6 and n = 4.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITExplain how you canuse a number line tocheck the results ofsubtracting integers.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEGEOGRAPHY In Mongolia, the temperature can fallto -45°C in January. The temperature in July mayreach 40°C. What is the difference between these twotemperatures in Mongolia?To find the difference in temperatures, subtract the lowertemperature from the higher temperature.40 - (-45) = 40 45 To subtract -45, 45.= Simplify.So, the difference between the temperatures is .Check Your Progress On a particular day in Anchorage,Alaska, the high temperature was 15°F and the lowtemperature was -11°F. What is the difference between thesetwo temperatures for that day?Math Connects, Course 2 45

2–6 Multiplying IntegersEXAMPLES Multiply Integers with Different SignsMAIN IDEA• Multiply integers.Find 5 (-4) .5 (-4) = The integers have signs.The product is .Find -3 (9) .-3 (9) = The integers have signs.The product is .Check Your Progress Multiply.a. 3 (-5) b. -5(7)KEY CONCEPTSMultiplying Integerswith Different Signs Theproduct of two integerswith different signs isnegative.Multiply Integers withthe Same Sign Theproduct of two integerswith the same sign ispositive.®Include theseconcepts on the Lesson2–6 tab of your FoldableEXAMPLES Multiply Integers with the Same SignFind -6(-8).-6(-8) = The integers have the sign.The product is .Find (-8) 2 .(-8) 2 = (-8) There are factors of -8.= The product is .Find -2(-5)(-6).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.-2 (-5) (-6) = (-6) -2 (-5) = 10= 10 (-6) = -6046 Math Connects, Course 2

2–6Check Your Progress Multiply.a. -4(-7) b. (-5) 2 c. -7(-3)(-4)EXAMPLEREMEMBER ITWhen threevariables are writtenwithout an operationssign, it meansmultiplication.MINES A mine elevator descends at a rate of 300 feetper minute. How far below the earth’s surface will theelevator be after 5 minutes?If the elevator descends feet per minute, then after 5minutes, the elevator will be -300 ( ) or -1,500 feet belowthe surface. Thus, the elevator will descend tofeet.Check Your Progress RETIREMENT Mr. Rodriguez has$78 deducted from his pay every month and placed in a savingsaccount for his retirement. What integer represents a change inhis savings account for these deductions after six months?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Evaluate ExpressionsALGEBRA Evaluate abc if a = -3, b = 5, and c = -8.abc = (-3)(5)(-8) Replace with -3, bwith , and c with .= (-15)(-8) Multiply and 5.= Multiply -15 and -8.Check Your ProgressEvaluate xyz if x = -6, y = -2, and z = 4.Math Connects, Course 2 47

2–7 Problem-Solving Investigation:Look for a PatternMAIN IDEA• Solve problems bylooking for a pattern.EXAMPLE Use the Look for a Pattern StrategyHAIR Lelani wants to grow an 11-inch ponytail. She hasa 3-inch ponytail now, and her hair grows about oneinch every two months. How long will it take for herponytail to reach 11 inches?UNDERSTAND You know the length of Lelani’s ponytail now.You know how long Lelani wants her ponytailto grow and you know how fast her hair grows.You need to know how long it will take for herPLANSOLVEponytail to reachinches.Look for a pattern. Then extend the pattern tofind the solution.After the first two months, Lelani’s ponytailwill be 3 inches +inch, or 4 inches.Every months, her hair growsaccording to the pattern below.3 in. 4 in. 5 in. 6 in. 7 in. 8 in. 10 in. 11 in.HOMEWORKASSIGNMENTPage(s):Exercises:CHECK+1 +1 +1 +1 +1 +1 +1It will take eight sets of two months, or 16months total, for Lelani’s ponytail to reachinches.Lelani’s ponytail grew from 3 inches to11 inches, a difference of eight inches, inmonths. Since one inch of growthrequires two months and 8 ×answer is correct.= 16, theCheck Your Progress RUNNING Samuel ran 2 mileson his first day of training to run a marathon. On the thirdday, Samuel increased the length of his run by 1.5 miles. Ifthis pattern continues every three days, how many miles willSamuel run on the 27 th day?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.48 Math Connects, Course 2

2–8 Dividing IntegersEXAMPLES Dividing Integers with Different SignsMAIN IDEA• Divide integers.KEY CONCEPTSDividing Integers withDifferent Signs Thequotient of two integerswith different signs isnegative.Dividing Integers withthe Same Sign Thequotient of two integerswith the same sign ispositive.Find 51 ÷ (-3) .51 ÷ (-3) = The integers have signs.Find _ -12111 .Theis negative._-121= The have different signs.11The quotient is .EXAMPLE Dividing Integers with the Same SignFind -12 ÷ (-2) .-12 ÷ (-2) = The integers have the sign.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:The quotient is .Check Your Progress Find each quotient.a. 36 ÷ (-9) b. _ 45c. -24 ÷ (-8)-9EXAMPLEALGEBRA Evaluate -18 ÷ x if x = -2.-18 ÷ x = -18 ÷ ( ) Replace x with -2.= Divide. The quotient is negative.Check Your Progress ALGEBRA Evaluate g ÷ h if g = 21and h = -3.Math Connects, Course 2 49

C H A P T E R2BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 2 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 2, go to:glencoe.comYou can use your completedVocabulary Builder(pages 32–33) to help yousolve the puzzle.2-1Integers and Absolute ValueExpress each of the following in words.1. +72. -73. ⎪7⎥4. On the following number line, draw an oval around the negativeintegers and label them negative. Draw a rectangle around thepositive integers and label them positive.2-2 Comparing and Ordering IntegersWrite each expression in words.5. -1 < 06. 3 > -2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.50 Math Connects, Course 2

Chapter 2 BRINGING IT ALL TOGETHER2-3The Coordinate PlaneLook at the coordinate plane at the right. Name the orderedpair for each point graphed.7. A8. B9. CA432O 1 2 3 4 xIn the coordinate plane above, identify the quadrant inwhich each lies.10. A4321234yCB11. B12. C2-4Adding IntegersCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Tell how you would solve each of the following on a numberline, then add.13. -7 + (-9)14. -7 + 915. How many units away from 0 is the number 17?16. How many units away from 0 is the number -17?17. What are 17 and -17 called?Math Connects, Course 2 51

Chapter 2 BRINGING IT ALL TOGETHER2-5Subtracting IntegersFind each difference. Write an equivalent addition sentencefor each.18. 1 - 519. -2 - 120. -3 - 42-6Multiplying IntegersChoose the correct term to complete each sentence.21. The product of two integers with different signs is (positive,negative).22. The product of two integers with the same sign is (positive,negative).Find each product.23. (-6) (-4) 24. -8 (5) 25. -2 (3) (-4)2-7Problem-Solving Investigation: Look for a Pattern26. CANS A display of soup cans at the end of a store aislecontains 1 can in the top row and 2 cans in each additionalrow beneath it. If there are 6 rows in the display, howmany cans are in the sixth row?2-8Dividing IntegersWrite two division sentences for each of the followingmultiplication sentences.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.27. 6 (-3) = 1828. -21 (-2) = 4252 Math Connects, Course 2

C H A P T E R2ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study are given witheach item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 2.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 2 Practice Test onpage 123 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 2 Study Guide and Reviewon pages 119–122 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 2 Practice Test onpage 123 of your textbook.I asked for help from someone else to complete the reviewof all or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 2 Foldables.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 2 Study Guide and Review onpages 119–122 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 123 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 53

C H A P T E R3Algebra: Linear Equations and Functions®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" × 17" paper.Fold the short sidestoward the middle.Fold the top to thebottom.Open . Cut along thesecond fold to makefour tabs.Label each of thetabs as shown.NOTE-TAKING TIP: When you take notes, listen orread for main ideas. Then record those ideas in asimplified form for future reference.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.54 Math Connects, Course 2

C H A P T E R3BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleAddition Propertyof EqualityDivision Propertyof EqualityCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.formulalinear equation(continued on the next page)Chapter 3Math Connects, Course 2 55

Chapter 3 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleSubtraction Propertyof Equalitytwo-step equationwork backwardstrategyCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.56 Math Connects, Course 2

3–1Writing Expressions and EquationsEXAMPLE Write a Phrase as an ExpressionMAIN IDEA• Write verbal phrasesand sentences as simplealgebraic expressionsand equations.Write the phrase twenty dollars less the price of a movieticket as an algebraic expression.Wordstwenty dollars less the price of amovie ticketVariableLet= the price of a movie ticket.EquationORGANIZE ITWrite two phrasesand their algebraicexpressions under theExpressions tab.®Check Your Progress Write the phrase five more inchesof snow than last year’s snowfall as an algebraic expression.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLES Write Sentences as EquationsWrite each sentence as an algebraic equation.A number less 4 is 12.Words A number less 4 is 12.Variable Let represent a number.EquationTwice a number is 18.Words Twice a number is 18.Variable Let represent a number.EquationMath Connects, Course 2 57

3–1Check Your Progress Write each sentence as analgebraic equation.a. Eight less than a number is 12.b. Four times a number equals 96.EXAMPLEFOOD An average American adult drinks more softdrinks than any other beverage each year. Three timesthe number of gallons of soft drinks plus 27 is equal tothe total 183 gallons of beverages consumed. Write theequation that models this situation.WordsThree times the number of gallons of softdrinks plus 27 equals 183.HOMEWORKASSIGNMENTPage(s):Exercises:VariableEquationLet= the number of gallons of soft drinks.Check Your Progress EXERCISE It is estimated thatAmerican adults spend an average of 8 hours per monthexercising. This is 26 hours less than twice the number of hoursspent watching television each month. Write an equation thatmodels this situation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.58 Math Connects, Course 2

3–2 Solving Addition and Subtraction EquationsEXAMPLES Solve an Addition EquationMAIN IDEA• Solve addition andsubtraction equations.Solve 14 + y = 20. Check your solution.14 + y = 20 Write the equation.14 from̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲each side. Simplify.=Check14 + y = 20 Write the original equation.KEY CONCEPTS14 + 20 Replace y with .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Subtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.Addition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.®Write theseproperties in yourown words under theEquations tab.= 20 ̌ Simplify.The solution is .Solve a + 7 = 6. Check your solution.a + 7 = 6 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲Subtract from each side.= Simplify.Checka + 7 = 6Write the original equation.+ 7 6 Replace a with .= 6 ̌ Simplify. The solution is.Check Your Progress Solve each equation.a. -6 = x + 4 b. m + 9 = 22Math Connects, Course 2 59

3–2EXAMPLEFRUIT A grapefruit weighs 11 ounces, which is 6 ouncesmore than an apple. How much does the apple weigh?WordsVariableA grapefruit’s is more an apple’sweight ounces than weight.Let a represent the apple’s weight.Equation11 = 6 + aREVIEW ITExplain why the sum ofthree negative numbersmust be negative.(Lesson 2-4)Write the equation.̲̲̲̲̲̲ -6 -6 Subtract from each side.5 = a Simplify.The apple weighsounces.Check Your Progress EXERCISE Cedric ran 17 milesthis week, which is 9 more miles than he ran last week. Howmany miles did he run last week?HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Solve a Subtraction EquationSolve 12 = z - 8.12 = z - 8 Write the equation.̲̲̲̲̲̲̲̲̲+ 8 + 8 Add 8 to each side.= z Simplify.The solution is .Check Your Progress Solve w - 5 = 27.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.60 Math Connects, Course 2

3–3 Solving Multiplication EquationsEXAMPLES Solving Multiplication EquationsMAIN IDEA• Solve multiplicationequations.Solve 39 = 3y. Check your solution.39 = 3y Write the equation.=Divide each side of the equation by .= y ÷ 3 =Check39 = 3y Write the equation.KEY CONCEPTDivision Property ofEquality If you divideeach side of an equationby the same nonzeronumber, the two sidesremain equal.39 3 Replace y with . Is this sentence true?39 = ̌So, the solution is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®Record theDivision Property ofEquality in your ownwords under theEquation tab.Solve -4z = 60. Check your solution.-4z = 60 Write the equation.Check= Divide each side of the equation by .z = 60 ÷ (-4) =-4z = 60 Write the equation.-4( ) 60 Replace z with . Is this sentence true?= 60 ̌So, the solution is .Math Connects, Course 2 61

3–3Check Your Progress Solve each equation. Check yoursolution.a. 6m = 42 b. -64 = -16bBUILD YOUR VOCABULARY (pages 55–56)A formula is an equation that shows the relationship amongcertain quantities.EXAMPLESWIMMING Ms. Wang swims at a speed of 0.6 mph. At thisrate, how long will it take her to swim 3 miles?You are asked to find the time t it will take to swim adistance d of 3 miles at a rate r of 0.6 mph.d = rt Write the equation.HOMEWORKASSIGNMENTPage(s):Exercises:3 = 0.6t Replace d with and r with .3__0.6 = 0.6t0.6Divide each side by 0.6.= t 3 ÷ 0.6 = 5It would take Ms. Wanghours to swim 3 miles.Check Your Progress COOKIES Debbie spends $6.85on cookies at the bakery. The cookies are priced at $2.74 perpound. How many pounds of cookies did Debbie buy?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.62 Math Connects, Course 2

3–4 Problem-Solving Investigation:Work BackwardEXAMPLE Use the Work Backward StrategyMAIN IDEA• Solve problems usingthe work backwardstrategy.SHOPPING Lucy and Elena went to the mall. Each girlbought a CD for $16.50, a popcorn for $3.50, and a drinkfor $2.50. Altogether, they had $5.00 left over. How muchmoney did they take to the mall?UNDERSTAND You know that they hadPLANSOLVEleft overand how much they spent on each item. Youneed to know how much they took to the mall.Start with the end result and work backward.They had $5.00 left.Undo the two drinks $5 + 2 ($2.50) =for $2.50 each.Undo the two popcorns $10 + 2 ($3.50) =foreach.Undo the two CDs for $17 + 2 ($16.50) =$16.50 each.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:CHECKSo, they tookto the mall.Assume they started with $50. After buyingtwo CDs, they had $50 - 2($16.50) or .After buying two popcorns, they had$17 - 2 ( ) or $10. After buying twodrinks, they had $10 - 2($2.50) or $5. So, theanswer is correct.Check Your Progress AIRPORT Jack needs to go homefrom work to pack before heading to the airport. He wants tobe at the airport by 1:15 P.M. It takes him 20 minutes to drivehome from work, 30 minutes to pack, and 45 minutes to get tothe airport from home. What time should he leave work?Math Connects, Course 2 63

3–5Solving Two-Step EquationsBUILD YOUR VOCABULARY (pages 55–56)MAIN IDEA• Solve two-stepequations.A two-step equation has different .EXAMPLES Solve Two-Step EquationsSolve 4x + 3 = 19. Check your solution.4x + 3 = 19 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲ Subtractfrom each side.= Simplify.= Divide each side by .= Simplify.CheckWRITE ITWhat is the name of theproperty that allows youto subtract the samenumber from each sideof an equation?4x + 3 = 19Write the original equation.4 ( ) + 3 19 Replace x with .+ 3 19 Simplify.= 19 ̌The solution is .Solve 6 + 5y = 26.Write the equation.̲̲̲̲̲̲̲̲̲-6 -6 Subtract from each side.5y = 20 Simplify._ 5y5 = _ 205Divide each side by .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.y =Simplify.64 Math Connects, Course 2

3–5Solve -3c + 9 = 3.-3c + 9 = 3 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲ Subtractfrom each side.= Simplify.= Divide each side by .= Simplify.The solution is .Solve 0 = 6 + 3t.0 = 6 + 3t Write the equation.̲̲̲̲̲̲̲̲̲̲̲-6 -6= Simplify.= each side by .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITAlways check yoursolutions by replacingthe variable with youranswer and simplifying.= Simplify.The solution is .Check Your Progress Solve each equation.a. 3t - 7 = 14 b. 4 + 2w = 18c. -8k + 7 = 31 d. 0 = -4x + 32Math Connects, Course 2 65

3–5EXAMPLEPARKS There are 76 thousand acres of state parkland inGeorgia. This is 4 thousand acres more than three timesthe number of acres of state parkland in Mississippi.How many acres of state parkland are there inMississippi?WordsVariableEquationThree times the number of acres of stateparkland in Mississippi plus 4,000 is 76,000.Let m = the acres of state parkland inMississippi.Three times thenumber of acresof parklandin Mississippi plus 4,000 is 76,000.4,000 = 76,000+ 4,000 = 76,000 Write the equation.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲ Subtracteach side.from= Simplify.HOMEWORKASSIGNMENTPage(s):Exercises:There are= Divide each side by .= Simplify.acres of state parkland in Mississippi.Check Your Progress BASEBALL Matthew had 64 hitsduring last year’s baseball season. This was 8 less than twicethe number of hits Gregory had. How many hits did Gregoryhave during last year’s baseball season?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.66 Math Connects, Course 2

3–6 Measurement: Perimeter and AreaMAIN IDEA• Find the perimetersand areas of figures.BUILD YOUR VOCABULARY (pages 55–56)Thearound a geometric figure is called theperimeter.EXAMPLE Find the Perimeter of a RectangleFind the perimeter of the rectangle.18 ftP = 2l + 2wPerimeter of a rectangle2 ftP = 2 (18) + 2 (2) l = , w =P = + Multiply.P =Add.The perimeter is 40 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTPerimeter of a RectangleThe perimeter P of arectangle is twice thesum of the length l andwidth w.Check Your Progress Find the perimeter of arectangle with a length of 2.35 centimeters and awidth of 11.9 centimeters.EXAMPLEART A painting has a perimeter of 68 inches. If the widthof the painting is 13 inches, what is its length?P = 2l + 2w68 = 2l + 2 ( )Perimeter of a rectangleReplace P with 68 and w with 13.68 = 2l + Multiply.(continued on the next page)Math Connects, Course 2 67

3–668 - 26 = 2l + 26 - 26 Subtract 26 from each side.= 2l Simplify.21 = l Divide each side by 2.Check Your Progress GARDENS A tomato garden hasa perimeter of 22.2 feet. If the length of the garden is 6.3 feet,find the width.BUILD YOUR VOCABULARY (pages 55–56)The area is the measure of thefigure.enclosed by aEXAMPLE Find The Area of a RectangleKEY CONCEPTFRESHWATER Find the area of the surface of thereservoir shown below.Area of a Rectangle Thearea A of a rectangle isthe product of the lengthl and width w.HOMEWORKASSIGNMENTPage(s):Exercises:A = l · wArea of aA = · Replace l with 4 and w with .A = .The area is 2.5 .Check Your ProgressPAINTING Sue is painting a wallthat measures 18.25 feet long and8 feet high. Find the area of thesurface Sue will be painting.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.68 Math Connects, Course 2

3–1 3–7Functions and GraphsEXAMPLEMAIN IDEA• Graph linear equations.REMEMBER ITWhen x and y areused in an equation,x usually representsthe input and y usuallyrepresents the output.WORK The table shows the number of hours Abbyworked and her corresponding earnings. Make a graphof the data to show the relationship between the numberof hours Abby worked and her earnings.The ordered pairs (1, 6) , ( , 12) , (3, ) , and (4, 24)represent the function. Graph the ordered pairs.Number ofHoursEarnings ($)1 62 123 184 24 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress VIDEOS Make a graph of the datain the table that shows the relationship between the amountDavid would pay and the number of movies he rents.Number ofVideosAmount ($)1 $3.502 $7.003 $10.504 $14.00 Math Connects, Course 2 69

3–7BUILD YOUR VOCABULARY (pages 55–56)An equation like y = 2x + 1 is a linear equation becausethe is a line.WRITE ITHow many points areneeded to graph a line?Why is it a good idea tograph more?EXAMPLE Graph Solutions of Linear EquationsGraph y = x + 3.Select any four values for the input x. We chose 2, 1, 0, and -1.Substitute these values for x to find the output y.x x + 3 y (x, y)2 + 3 (2, 5)1 + 3 40 0 + 3-1 + 3 2y(0, 3)(1, 2)O(2, 5) Four solutions are(1, 4)x(2, 5) ,,and .Check Your Progress Graph y = 3x - 2.yOx,Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.70 Math Connects, Course 2

3–7EXAMPLE Represent Real-World FunctionsANIMALS Blue whales can reach a speed of 30 milesper hour. The equation d = 30t describes the distanced that a whale swimming at that speed can travel intime t. Assuming that a whale can maintain that speed,represent the function with a graph.Step 1 Select four values for t. Select only positive numberssince t represents time. Make a function table.t 30t d (t, d)2 30 (2) (2, 60)3 30 (3) 905 30 (5)6 30 180Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Step 2 Graph the orderedpairs and draw aline through thepoints.Distance (mi)35030025020015010050dBlue Whales(3, 90)(2, 60)(6, 180)(5, 150)0 1 2 3 4 5 6 7Time (h)Check Your Progress TRAVEL Susie takes a car triptraveling at an average speed of 55 miles per hour. Theequation d = 55t describes the distance d that Susietravels in time t. Represent this function with a graph.Distance (mi)25020015010050yCar Tript0 1 2 3 4 5Time (h)xMath Connects, Course 2 71

C H A P T E R3BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go to:glencoe.comYou can use your completedVocabulary Builder(pages 55–56) to help yousolve the puzzle.3-1Writing Expressions and EquationsMatch the phrases with the algebraic expressions thatrepresent them.1. seven plus a number a. 7 - n2. seven less a number3. seven divided by a number4. seven less than a numberb. 7 · nc. n - 7d. n_7e. 7 + nWrite each sentence as an algebraic equation.5. The product of 4 and 6. Twenty divided bya number is 12. y is equal to -10.3-2Solving Addition and Subtraction Equations7. Explain in words how to solve a - 10 = 3.Solve each equation. Check your solution.8. w + 23 = -11 9. 35 = z - 15Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.72 Math Connects, Course 2

Chapter 3 BRINGING IT ALL TOGETHER3-3Solving Multiplication Equations10. To solve -27 = -3d, divide each side by .Solve each equation. Check your solution.11. 36 = 6k 12. -7z = 283-4Problem-Solving Investigation: Work Backward13. AGE Bradley is four years older than his brother Philip. Philip is7 years younger than Kailey, who is 2 years older than Taneesha.If Taneesha is 11 years old, how old is Bradley?3-5Solving Two-Step EquationsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14. Describe in words each step shown for solving 12 + 7s = -9.12 + 7s = -9̲̲̲̲̲̲̲̲̲̲-12 -127s = -21_ 7s7 = _-217s = -315. Number the steps in the correct order for solving the equation-4v + 11 = -5.SimplifyDivide each side by -4.Write the equation.Simplify.Subtract 11 from each side.Check the solution.Math Connects, Course 2 73

Chapter 3 BRINGING IT ALL TOGETHER3-6Measurement: Perimeter and AreaFind the perimeter and area of each rectangle.16.17.18. FRAMING Marcia wants to frame her favorite painting. If theframe is 3.25 feet wide and the perimeter is 15.7 feet, find thewidth of the frame.3-7Functions and Graphs19. Complete the function table. Then graph the function.x 2x - 1 yy-101OxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.74 Math Connects, Course 2

C H A P T E R3ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 3.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 3 Practice Test on page 173of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 3 Study Guide and Reviewon pages 169–172 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 3 Practice Test on page 173.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 3 Foldable.• Then complete the Chapter 3 Study Guide and Review onpages 169–172 of your textbook.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 3 Practice Test onpage 173.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 75

C H A P T E R4 Fractions, Decimals, and Percents®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 8 _ 1 " × 11" paper.2Stack five sheets ofpaper 3_ inch apart.4Roll up bottom edgesso that all tabs are thesame size.Crease and staplealong the fold.Write the chapter titleon the front. Labeleach tab with a lessonnumber and title.NOTE-TAKING TIP: Before each lesson, skimthrough the lesson and write any questions thatcome to mind in your notes. As you work throughthe lesson, record the answer to your question.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.76 Math Connects, Course 2

C H A P T E R4BUILD YOUR VOCABULARYChapter 4This is an alphabetical list of new vocabulary terms you will learn in Chapter 4.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebar notationcommon denominatorcomposite number[kahm-PAH-zuht]Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.equivalent[ih-KWIH-vuh-luhnt]fractionsfactor treegreatest common factor(GCF)least commondenominator (LCD)least common multiple(LCM)multiple(continued on the next page)Math Connects, Course 2 77

Chapter 4 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplepercentprime factorizationprime numberratiorational numberrepeating decimalsimplest formterminating decimalCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.78 Math Connects, Course 2

4–1Prime FactorizationMAIN IDEA• Find the primefactorization of acomposite number.BUILD YOUR VOCABULARY (pages 77–78)A prime number is a whole number greater than 1 thathas exactly factors, and .A composite number is a whole number greater thanthat has more thanfactors.Everynumber can be written as a productof prime numbers exactly one way called the primefactorization.A factor tree can be used to find the factorization.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITUnder the tab forLesson 4-1, give examplesof prime and compositenumbers. Be sure toexplain how to tell aprime number from acomposite number.EXAMPLES Identify Numbers as Prime or CompositeDetermine whether each number is prime or composite.6363 has six factors: 1, , 7, , 21, and .So, it is .2929 has only two factors: and .So, it is .Check Your Progress Determine whether each numberis prime or composite.a. 41 b. 24Math Connects, Course 2 79

4–1EXAMPLE Find the Prime FactorizationREMEMBER ITMultiplication iscommutative, so theorder of factors doesnot matter.Find the prime factorization of 100.To find the prime factorization, you can use a factor tree ordivide by prime numbers. Let’s use a factor tree.100× 225 × ×× × ×100 = × × × or × .EXAMPLE Find an Algebraic ExpressionALGEBRA Factor 21 m 2 n.HOMEWORKASSIGNMENTPage(s):Exercises:21 m 2 n21 ×× 7 × × n× × × ×Check Your Progressa. Find the prime factorization of 72.b. Factor 15x y 3 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.80 Math Connects, Course 2

4–2Greatest Common FactorMAIN IDEA• Find the greatestcommon factor of twoor more numbers.BUILD YOUR VOCABULARY (pages 77–78)A Venn diagram usesto show how elementsamong sets of numbers or objects are related.Thenumber that is a commonto two or more numbers is called the greatest commonfactor (GCF).EXAMPLE Find the Greatest Common Factor®ORGANIZE ITUnder the tab forLesson 4-2, take noteson finding the greatestcommon factor of two ormore numbers.Find the GCF of 28 and 42.METHOD 1 First, list the factors of 28 and 42.factors of 28:factors of 42:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The common factors are .So, the GCF is .METHOD 2 Use prime factorization.28 = 2 × 2 ×42 = 2 × 3 ×The greatest common factor or GCF is 2 × 7 or .Check Your Progress Find the GCF of 18 and 45.Math Connects, Course 2 81

4–2EXAMPLE Find the GCF of Three NumbersWRITE ITWhich method of findingthe GCF of two or morenumbers do you preferusing to find the GCF ofsmall numbers? for largenumbers?Find the GCF of 21, 42, and 63.METHOD 1 First, list the factors of 21, 42, and 63.factors of 21: 1, 3, 7,factors of 42: 1, 2, 3, 6, 7, 14, 21, 42factors of 63: 1, 3, , 9, 21, 63The common factors of 21, 42, and 63 are , , and .So, the greatest common factor or GCF is .METHOD 2 Use prime factorization.21 = 3 × 742 = 2 × 3 × 7 Circle the common factors.63 = 3 × 3 × 7The common prime factors are 3 and 7.The GCF is × , or .Check Your Progressof numbers.24, 48, and 60EXAMPLEFind the GCF of each setART Searra wants to cut a 15-centimeter by25-centimeter piece of tag board into squaresfor an art project. She does not want to wasteany of the tag board and she wants the largestsquares possible. What is the length of the sideof the squares she should use?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.82 Math Connects, Course 2

4–2The largest length of side possible is the GCF of the dimensionsof the tag board.15 = ×25 = ×The of 15 and 25 is . So, Searra should usesquares with sides measuringcentimeters.EXAMPLEHow many squares can she make if the sides are5 centimeters?÷ 5 = 5 squares can fit along the length.÷ 5 = 3 squares can fit along the width.So, 5 × 3 =squares can be made from the tag board.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress CANDY Alice is making candybaskets using chocolate hearts and lollipops. She is tying eachpiece of candy with either a red piece of string or a green pieceof string. She has 64 inches of red string and 56 inches of greenstring. She wants to cut the pieces of string equal lengths anduse all of the string she has.a. What is the length of the longest piece of string thatcan be cut?b. How many pieces of string can be cut if the pieces are8 inches long?Math Connects, Course 2 83

4–3 Problem-Solving Investigation:Make an Organized ListEXAMPLE Make an Organized ListMAIN IDEA• Solve problems bymaking an organizedlist.PASSWORD In order to log on to the computer atschool, Miranda must use a password. The passwordis 2 characters. The first character is the letter A or Bfollowed by a single numeric digit. How many passwordsdoes Miranda have to choose from?UNDERSTAND You know that the password hascharacters and that the first character is eitherthe letteror B. You know that the secondcharacter is a numeric digit. You need to knowhow many passwords can be created.PLANMake an organized list.SOLVEA B A B A B B A BHOMEWORKASSIGNMENTPage(s):Exercises:0 0 1 2 2 3 3 4 4A B A B A A B A B5 5 6 7 7 8 8 9 9CHECKThere arepasswords.Draw a tree diagram to check the result.Check Your Progress DELI At a deli, customers canchoose from ham or turkey on wheat, rye, or multi-grain bread.How many sandwich possibilities are there?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.84 Math Connects, Course 2

4–4 Simplifying FractionsMAIN IDEA• Write fractions insimplest form.BUILD YOUR VOCABULARY (pages 77–78)Fractions having the sameare calledequivalent fractions.A fraction is in simplest form when the greatest commonfactor of the and the denominator is 1.EXAMPLES Write Fractions in Simplest Form®ORGANIZE ITUnder the tab forLesson 4-4, take notesabout simplifyingfractions. Be sure toinclude an example.Write each fraction in simplest form._ 1245To write a fraction in simplest form, you can divide by commonfactors or divide by the . Let’s divide by the GCF.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.First, find the GCF of thefactors of 12:factors of 45:The GCF of 12 and 45 is ..andThen, divide the numerator and the denominator by .12 ÷12_45 = __ =45 ÷So, 12_ written in simplest form is4_45 15 .Math Connects, Course 2 85

4–4_ 4064factors of 40: 1, 2, , 5, 8, 10, 20,factors of 64: 1, 2, 4, 8, , 32, 64The GCF of 40 and 64 is .40 ÷_ 4064 = __ =64 ÷So, _ 40 written in simplest form is .64Check Your Progresssimplest form.a. _ 3240Write each fraction inb. 28 _49EXAMPLEHOMEWORKASSIGNMENTPage(s):Exercises:MUSIC Two notes form a perfect fifth if the simplifiedfraction of the frequencies of the notes equals _ 3 . If note4D = 294 Hertz and note G = 392 Hertz, do they form aperfect fifth?____frequency of note Dfrequency of note G =1 1 12= ____× 3 × 7 × 72 × 2 × 2 × 7 × 7 =1 1 1The fraction of the frequency of the notes D and G is .So, the two notes do form a perfect fifth.Check Your Progress In a bag of 96 marbles, 18 of themarbles are black. Write the fraction of black marbles insimplest form.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.86 Math Connects, Course 2

4–5 Fractions and DecimalsEXAMPLES Use Mental MathMAIN IDEA• Write fractionsas terminating orrepeating decimalsand write decimals asfractions.Write each fraction or mixed number as a decimal.9_10THINK× 109_10 =× 10So, 9 _10 = .7 3 _57 _ 3 = 7 + Think of it as a sum.5= 7 + You know that 3 _5 = 0.6.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the tab forLesson 4-5, take noteson writing fractions asdecimals and writingdecimals as fractions.Include examples.®= 7.6 Add mentally.So, 7 3 _5 = .Check Your Progressnumber as a decimal.a. _ 725b. 9 1_5Write each fraction or mixedMath Connects, Course 2 87

4–5EXAMPLE Use Pencil and Paper or a CalculatorWrite _ 1 as a decimal.8METHOD 1 Use paper and pencil.0.1258 1.000 Divide by .__ - 820___ - 1640___ - 400 Division ends when the remainder is 0.WRITE ITWrite the followingdecimal equivalents:1_2 , 1_3 , 2_3 , 1_4 , 3_4 , 1_5 , 1_10 , 1_8 .METHOD 2 Use a calculator.1 8 ENTERSo, 1_8 = .Check Your Progressnumber as a decimal.a. 2_5Write each fraction or mixedb. 1 7 _20BUILD YOUR VOCABULARY (pages 77–78)A terminating decimal is a decimal whose digits .Repeating decimals have a pattern in the digits thatrepeats .Bar notation is used to indicate that a number repeatsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.forever by writing athat repeat.over the88 Math Connects, Course 2

4–5EXAMPLES Write Fractions as Repeating DecimalsWrite1_ as a decimal.11METHOD 1 Use paper and pencil.0.0909...11 1.0000__ 0100____10__0____ 99METHOD 2 Use a calculator.1 11 ENTER 0.0909...So, 1_11 = .Check Your Progress Write 25_ as a decimal.11Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Use a Power of 10CEREAL Jorge read that 0.72 of his favorite cereal waswhole-grain wheat. Find what fraction of his cereal, insimplest form, is whole-grain wheat.0.72 = _ 72 The fi nal digit, , is in the hundredths place.100= _ 18 Simplify.25So,of the cereal is whole-grain wheat.Check Your Progress EXERCISE Jeanette ran 0.86 of amile. What fraction of a mile did she run?Math Connects, Course 2 89

4–6 Fractions and PercentsMAIN IDEA• Write fractions aspercents and percentsas fractions.BUILD YOUR VOCABULARY (pages 77–78)A ratio is aof two numbers by.When a compares a number to , it canbe written as a percent.EXAMPLES Write Ratios as PercentsKEY CONCEPTPercent A percent is aratio that compares anumber to 100.Write each ratio as a percent.Diana scored 63 goals out of 100 attempts.You can represent 63 outof 100 with a model.63_100 =In a survey, 31.9 out of 100 people on average preferredcrunchy peanut butter.__ 31.9=Check Your Progress Write each ratio as a percent.a. Alicia sold 34 of the 100 cookies at the bake sale.b. On average, 73.4 out of 100 people preferred the chickeninstead of the roast beef.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.90 Math Connects, Course 2

®ORGANIZE ITUnder the tab forLesson 4-6, take noteson writing fractions aspercents and percentsas fractions. Includeexamples.EXAMPLE Write a Fraction as a Percent_Write 16 as a percent.25Since 100 ÷ 25 = 4, . . .× 416_25 = _ 64100× 464_100 = 64%So, _ 1624 = 64%.4–6. . . multiply thenumerator anddenominator by 4.Check Your Progress Write11_ as a percent.20EXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:FISHING William caught and released 20 trout on hisfishing trip. Twelve of them were rainbow trout. Whatpercent of the trout he caught were rainbow trout?William caughtrainbow trout out of 20 trout.12_20 = Write an equivalent fraction with adenominator of 100.So,= 60%60_100 = 60%of the trout William caught were rainbow trout.Check Your Progress READING Mitchell read 18 out of25 chapters of a book during his winter vacation. What percentof chapters did he read?Math Connects, Course 2 91

4–7 Percents and DecimalsEXAMPLES Write Percents as DecimalsMAIN IDEA• Write percents asdecimals and decimalsas percents.Write 47.8% as a decimal.To write a percent as a decimal, you can either first writethe percent as aor divide mentally. Let’s dividementally.47.8% = 47.8 Remove the % symbol and divide by 100.= 0.478 Add leading zero.So, 47.8% = .POPULATION According to the Administration on Aging,about 28 _ 1 % of the population of the United States is519 years of age or younger. Write 28 _ 1 % as a decimal.528 1_ % = 28.2%5Write1_as 0.2.5= 28.2 Remove the % symbol and divide by 100.KEY CONCEPTWriting Percents asDecimals To write apercent as a decimal,divide the percent by 100and remove the percentsymbol.= Add leading zero.So, 28 1_5 % = 0.282.Check Your Progressa. Write 83.2% as a decimal.b. AMUSEMENT PARKS A popular amusement park reportsthat 17 _ 1 % of its visitors will return at least three times10during the year. Write 17 _ 1 % as a decimal.10Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.92 Math Connects, Course 2

4–7EXAMPLE Write Decimals as PercentsWrite 0.33 as a percent.METHOD 1 Write the decimal as a fraction.0.33 = _ 33100= Write the fraction as a percent.METHOD 2 Multiply mentally.0.33 = 33.0 Multiply by 100.= 33% Add the % symbol.So, 0.33 = .Check Your ProgressWrite 0.7 as a percent.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEPOPULATION In 1790, about 0.05 of the population of theUnited States lived in an urban setting. Write 0.05 as apercent.0.05 = Defi nition of decimal= Defi nition ofCheck Your Progress In 2000, the population of Illinoishad increased by 0.086 from 1990. Write 0.086 as a percent.Math Connects, Course 2 93

4–8 Least Common MultipleMAIN IDEA• Find the least commonmultiple of two ormore numbers.BUILD YOUR VOCABULARY (pages 77–78)A multiple is theof a number and anynumber.The least common multiple (LCM) of two or morenumbers is theof their common multiples,excluding .EXAMPLES Find the LCM®ORGANIZE ITUnder the tab forLesson 4-8, take notesabout least commonmultiples. Be sure toinclude examples.Find the LCM of 4 and 6.METHOD 1 List the nonzero multiples.multiples of 4:multiples of 6:The common multiples are , 24, 36, ... .The LCM of 4 and 6 is .METHOD 2 Use prime factorization.4 = ·Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6 = ·The LCM is 2 · 2 · 3 or .94 Math Connects, Course 2

4–8Find the LCM of 4 and 15.Use Method 2. Find the prime factorization of each number.4 = × 2 or15 = ×The prime factors of 4 and 15 are .The LCM of 4 and 15 is × 3 × 5, or .Check Your Progress Find the LCM of each setof numbers.a. 8, 12 b. 6, 14EXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:WORK On an assembly line, machine A must be oiledevery 18 minutes, machine B every 24 minutes, andmachine C every 48 minutes. If all three machines areturned on at the same time, in how many minutes willall three machines need to be oiled at the same time?First find the LCM of 18, 24, and 48.18 = 2 × 3 × 3 or 2 × 3 224 = 2 × 2 × 2 × 3 or 2 3 × 348 = 2 × 2 × 2 × 2 × or 2 4 × 3The LCM of 18, 24, and 48 is 2 4 × 3 2 or × 9, which is 144.So, all three machines will need to be oiled at the same time inminutes.Check Your Progress LIGHTS Brenda put up threedifferent strands of decorative blinking lights. The first strandblinks every 6 seconds while the second strand blinks every 8seconds. The third strand blinks every 4 seconds. If all strandsblink at the same time, in how many seconds will they againblink at the same time?Math Connects, Course 2 95

4–9 Comparing and Ordering Rational NumbersMAIN IDEA• Compare and orderfractions, decimals, andpercents.BUILD YOUR VOCABULARY (pages 77–78)Rational numbers are numbers that can be written asfractions and include fractions, terminating and repeatingdecimals, and .A common denominator is a common multiple of two ormore .The least common denominator (LCD) is theof the denominators.EXAMPLES Compare Rational NumbersReplace 3_each with , or = to make a true sentence.7_-3 -38 8Graph each rational number on a number line.REVIEW ITExplain how to write 48_60as a decimal.(Lesson 4-5)Mark off equal size increments of between -4 and .The number line shows that -3 3_85_12 _ 716-3 7_8 .The LCD of the denominators, 12 and 16, is 48.5_12 = 5 ·12 ·7_ 16 = 7 ·16 · ____ = _48= _48 Since < , then 5 _12 7_16 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.96 Math Connects, Course 2

4–9Check Your Progressmake a true sentence.a. -2 4_ 5 -2 3_ 5Replace each with , or = tob. _ 5 8 _ 712EXAMPLEKEY CONCEPTRational NumbersRational numbers arenumbers that can bewritten as fractions.®Takes notes onrational numbers. Be sureto include examples.DOGS According to the Pet Food Manufacturer’sAssociation, 11 out of 25 people own large dogs and 13out of 50 people own medium dogs. Do more people ownlarge or medium dogs?Write 11_ 25 and _ 13 as decimals and compare.5011_25 = 13_50 =Since 0.44 > 0.26, 11_2513_50 .So, a greater fraction of people owndogs thanowndogs.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress A survey showed that 21 out of 50people stated that summer is their favorite season and 13 out of25 people prefer fall. Do more people prefer summer or fall?Math Connects, Course 2 97

C H A P T E R4BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 4 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 4, go to:glencoe.comYou can use your completedVocabulary Builder(pages 77–78) to help yousolve the puzzle.4-1Prime FactorizationUnderline the correct terms to complete each sentence.1. A factor tree is complete when all of the factors at the bottom ofthe factor tree are (prime, composite) factors.2. The order of the factors in prime factorization(does, does not) matter.Find the prime factorization of each number.3. 36 4. 485. 250 6. 604-2Greatest Common FactorComplete each sentence.7. A shows how elements of sets of numbersare related.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8. A prime factor is a factor that is a number.98 Math Connects, Course 2

Chapter 4 BRINGING IT ALL TOGETHER9. You can find the of two numbers bythe common prime factors.Find the common prime factors and GCF of each set ofnumbers.10. 20, 24 11. 28, 424-3Problem-Solving Investigation: Make an Organized List12. CLOTHES Lucas has a pair of brown pants and a pair of blackpants. He has a white dress shirt, a blue dress shirt, and a tandress shirt. He has a striped tie and a polka-dotted tie. Assuminghe can wear any combination, how many combinations of one pairof pants, one dress shirt, and one tie can Lucas wear?4-4Simplifying FractionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Complete the sentence.13. To find the simplest form of a fraction, the numeratorand the denominator by the .Write each fraction in simplest form.14. _ 18244-5Fractions and Decimals15. 15 _60Write each fraction or mixed number as a decimal. Use barnotation if the decimal is a repeating decimal.16. 3 2_319. 7 3 _817. 5 3 _420. 6 1_218. 2_521. 7 _10Math Connects, Course 2 99

Chapter 4 BRINGING IT ALL TOGETHER4-6Fractions and Percents22. Write the ratio that compares 4 to 25 in three different ways.23. Write the ratio in exercise 23 as a percent.24. Write 88% as a fraction in simplest form.25. Write _ 9 as a percent.204-7Percents and DecimalsWrite each percent as a decimal.26. 69% 27. 3% 28. 32 1_4 %Write each decimal as a percent.29. 0.47 30. 0.5775 31. 0.094-8Least Common MultipleFind the LCM of each set of numbers.32. 15, 36 33. 21, 7034. 16, 20 35. 6, 9, 2436. 12, 18, 30 37. 14, 28, 354-9Comparing and Ordering Rational NumbersReplace each with , or = to make each sentence true.38. 14_35 12_2039. 21_49 _ 1863Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.100 Math Connects, Course 2

C H A P T E R4ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 4.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 4 Practice Test on page 225of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 4 Study Guide and Reviewon pages 221–224 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 4 Practice Test onpage 225 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 4 Foldables.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 1 Study Guide and Review onpages 221–224 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 4 Practice Test onpage 225 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 101

C H A P T E R5 Applying Fractions®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" by 17" paper, four indexcards, and glue.Fold the paper in halfwidthwise.Open and fold alongthe length about 2 1_ "2from the bottom.Glue the edges on eitherside to form two pockets.Label the pockets Fractionsand Mixed Numbers,respectively. Place twoindex cards in each pocket.NOTE-TAKING TIP: When you take notes, place aquestion mark next to any concepts you do notunderstand. Be sure to ask your teacher to clarifythese concepts before a test.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.102 Math Connects, Course 2

C H A P T E R5BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 5.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecompatible numbersChapter 5like fractionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.multiplicative inverse[MUHL-tuh-PLIH-kuh-tihv]reciprocal[rih-SIH-pruh-kuhlunlike fractionsMath Connects, Course 2 103

5–1Estimating with FractionsEXAMPLES Estimate with Mixed NumbersMAIN IDEA• Estimate sums,differences, products,and quotients offractions and mixednumbers.Estimate.5 _ 1 4 + 3 _ 5 85 1_4 + 3 _ 5 85 + =The sum is about .7 _ 3 4 × 1 _ 7 87 _ 3 4 × 1 _ 7 8× =The sum is about .Check Your Progressa. 2 _ 7 9 + 5 1_4Estimate.b. 4 2_3 × 3 1_8®ORGANIZE ITRecord main ideas,definitions and othernotes about estimatingwith fractions on studycards. Store these cardsin the “Fractions” pocketof your Foldable.EXAMPLES Estimate with FractionsEstimate.1_3 + _ 4 71_3 + 4_71 is about 1.3 24 is about 1 .7 2+ =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The sum is about .104 Math Connects, Course 2

REMEMBER ITSome fractions areeasy to round becausethey are close to 1.Examples of these kindsof fractions are oneswhere the numeratoris one less than thedenominator, such as4_5or7_8 .5_8 - _ 1 40 5180 1145_8 - 1_4- =5 is about 1 .8 214is about 0.5–1The difference is about .5_6 ÷ _ 4 55_6 ÷ _ 3 4 ≈ ÷ = 15_6 ≈ and _ 3 4 ≈ .Check Your Progressa. _ 8 9 + 1_6b. 11_12 - 2_9Estimate.c. _ 3 5 ÷ _ 7 8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:BUILD YOUR VOCABULARY (page 103)Numbers that are easy to computecalled compatible numbers.EXAMPLE Use Compatible NumbersEstimate _ 3 × 21 using compatible numbers.4are3_4 × 21 ≈ _ 3 4 × 20 or Round 21 to 20, since 20is divisible by 4.Check Your Progress Estimate2_ × 17 using compatible3numbers.Math Connects, Course 2 105

5–2 Adding and Subtracting FractionsEXAMPLES Add and Subtract Like FractionsMAIN IDEA• Add and subtractfractions.KEY CONCEPTAdding and SubtractingLike Fractions To add orsubtract like fractions,add or subtract thenumerators and writethe result over thedenominator. Simplify ifnecessary.Add or subtract. Write in simplest form.7_12 + _ 4127_12 + 4_12 = ___125_6 - _ 1 6=5_6 - 1_6 = ___6Add the .Write the sum over thedenominator.numerators.the= orWrite the difference sover the. Simplify.EXAMPLES Add and Subtract Unlike FractionsAdd or subtract. Write in simplest form.1_3 + _ 1 9To add or subtract unlike fractions, you can use athe. Let’s use the LCD.The least common denominator of 3 and 9 is .1_3 = ___ 1 × 3= _ 3 91_3+ 1_9 _Rename 1_ using the .3+ 1_9 __ So, 1_3 + 1_9 = .orCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.106 Math Connects, Course 2

WRITE ITExplain what happensto denominators whenadding like fractions.3_4 - _ 1 6The LCD of 4 and 6 is .3_4_ 3 × 34 × 3_12Rename each fractionusing the LCD.5–2- 1_ _ 1 × 2__ 6 ___ 6 × 2-____ 12So, 3 _4 - 1_ 6 = .Check Your Progresssimplest form.a. _ 715 + 4_15b. _ 3 8 + 1_4Add or subtract. Write inc. _ 7 9 - 1_6Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEART A picture mounted on art board is _ 1 inch thick. The8frame for the picture is _ 1 inch thick. How much thicker2than the picture is the frame?The phrase how much thicker suggests, sofind 1_2 - 1_8 .1_2 - 1_ = - Rename the fractions using the LCD.8= 3 _8The frame isSubtract the numerators.inch thicker than the picture.Check Your Progress RUNNING Gregory ran3_ of a mile4on Monday and _ 5 of a mile on Tuesday. How much more of a6mile did he run on Tuesday?Math Connects, Course 2 107

5–3 Adding and Subtracting Mixed NumbersEXAMPLES Add and Subtract Mixed NumbersMAIN IDEA• Add and subtractmixed numbers.Add or subtract. Write in simplest form.3 _ 112 + 14 _ 712Estimate 3 + 15 =3 1_ 12 Add the whole numbers andfractions separately.+14_7___ 12or9 _ 710 - 4 _ 3 5Estimate 10 - 5 =Simplify. Compare the sumto the estimate.ORGANIZE ITRecord main ideas,definitions, and othernotes about addingand subtracting mixednumbers on study cards.Store the cards in the“Mixed Numbers” pocketof your Foldable.®9 _ 7__ 109 7 _10-4_3__ 5 ____Rename the fractionusing the .Simplify. Compare the sumto the estimate.EXAMPLES Rename Mixed Numbers to SubtractSubtract. Write in simplest form.8 _ 1 5 - 3 _ 3 58 1_57 6 _5- 3_3 - 3_3__ 5 ____ 5Rename 8 1_5 as .First subtract theand then the .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.108 Math Connects, Course 2

11 - 8 2 _35–311- 8 2_ 3̲̲̲- 8 _ 2 3̲̲̲̲̲Subtract.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITWhen you are addingmixed numbers, you canadd the whole numbersfirst and then add thefractions. Make sureif the fractions add tomore than one, that youchange the sum of thewhole numbers.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progresssimplest form.a. 5 _ 514 + 4 _ 314EXAMPLEAdd or subtract. Write inb. 6 2_9 - 3 _ 5 9c. 9 _ 3 8 - 5 _ 3 4COOKING A quiche recipe calls for 2 _ 3 cups of grated4cheese. A recipe for quesadillas requires 1 _ 1 cups of3grated cheese. What is the total amount of grated cheeseneeded for both recipes?2 _ 3 4 + 1 1_3 = 2 _ 912 + 1 4_12= +Rename the fractions.Add whole numbers andadd fractions._= 3 + 1_112 or Rename 1312simplify.The total amount of grated cheese needed isas 11_12 andcups.Check Your Progress TIME Jordan spent 31_ hours at the6mall and 2 1_ hours at the movies. How many more hours did he4spend at the mall than at the movies?Math Connects, Course 2 109

5–4 Problem-Solving Investigation:Eliminate PossibilitiesEXAMPLE Eliminate PossibilitiesMAIN IDEA• Solve problemsby eliminatingpossibilities.GAMES On a television game show, the winningcontestant must answer three questions correctly towin the grand prize. Each question is worth twice asmany points as the question before it. The third questionis worth 1,000 points. How much is the first questionworth—250, 500, or 2,000 points?UNDERSTAND You know that there are three questions andeach question is worthas manypoints as the question before it. You know thatthe third question is worth 1,000 points.PLANEliminate answers that are not.SOLVEThe first question cannot be worth 2,000 pointssince each question after it would have toworth more than 2,000 points, and the thirdHOMEWORKASSIGNMENTPage(s):Exercises:CHECKquestion is onlypoints. So, eliminatethat choice. If the first question is worth 500points, then the second question would beworth 1,000 points and the third questionwould be worthpoints. So, eliminatethat choice. The reasonable answer is 250points.If the first question is worth 250 points, thenthe second question would be worthpoints, and the third question would be worth1,000 points. So, the answer is correct.Check Your Progress CELL PHONES A cell phonecompany charges $35 for 500 free minutes and $0.50 for eachadditional minute. Using this plan, what is a reasonable price acustomer would pay for using 524 minutes—$32, $40, or $47?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.110 Math Connects, Course 2

5–5Multiplying Fractions and Mixed NumbersEXAMPLES Multiply FractionsMAIN IDEA• Multiply fractions andmixed numbers.Multiply. Write in simplest form.1_8 × _ 1 91_8 × 1_9 = Multiply the numerators.Multiply the denominators.= Simplify.6 × _ 1 36 × 1_3 = × 1_3= _ 6 × 11 × 3Write 6 as .Multiply the numeratorsand the denominators.= or Simplify.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTMultiplying FractionsTo multiply fractions,multiply the numeratorsand multiply thedenominators.®Take notes onmultiplying fractions andmixed numbers. Placeyour study cards in yourFoldable.Check Your Progressa. 1_5 × 1_7Multiply. Write in simplest form.b. 12 × 1_6EXAMPLE Simplify Before MultiplyingMultiply. Write in simplest form.3_12 × _ 4 5× 41_53_12 × 4_5 = _ 3123= ___Divide 4 and 12 by their GCF, 4.Multiply the numeratorsand the denominators.= Simplify.Math Connects, Course 2 111

5–5REMEMBER ITThe DistributiveProperty can help youdo mental math. Whenyou see a problem like1_4 · 4 4_“What is 1_4, you can think,9of 4 andwhat is 1_4of4_9?” This isequal to 1_4 (4 + 4_9) .EXAMPLE Multiply Mixed NumbersMultiply _ 1 3 × 6 _ 6 . Write in simplest form.7METHOD 1 Rename the mixed number.1_3 × 6 _ 6 7 = 1_31× 4816_7= __1 × 7Rename 6 _ 6 as an7Multiply.fraction, .= or Simplify.METHOD 2 Use mental math.1_3 × 6 6 _7 = 1_3 × ( + )Write 6_6 as a sum of7its parts.= ( 1_3 × 6 ) + ( 1_3 × 6 _7) Property= + or Multiply.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progressa. 4_9 × _ 6 7b. 1_6 × 4 _ 6 9Multiply. Write in simplest form.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.112 Math Connects, Course 2

5–6 Algebra: Solving EquationsMAIN IDEA• Solve equations withrational numbersolutions.BUILD YOUR VOCABULARY (page 103)Two numbers whose is are calledmultiplicative inverses.Reciprocals is another name given to.EXAMPLES Find Multiplicative InversesKEY CONCEPTMultiplicative InverseProperty The productof a number and itsmultiplicative inverse is 1.Find the multiplicative inverse of each number.4_74_7 · = 1 Multiply 4_ by to get the7product 1.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The multiplicative inverse of 4_ is , or .76 1 _46 1_4 = Rename the as animproper fraction.25_425· = 1 Multiply _ by to get the product 1.4The multiplicative inverse of 6 1_4 is .Check Your Progressof each number.a. _ 5 8Find the multiplicative inverseb. 4 1_3Math Connects, Course 2 113

5–6KEY CONCEPTMultiplication Propertyof Equality If youmultiply each side of anequation by the samenonzero number, the twosides remain equal.EXAMPLE Solve a Division EquationSolve 11 = _ p . Check your solution.611 = _ p 6Write the equation.11 · = _ p ·6Multiply each side by .= p Simplify.Check11 = p _611 = __6Write the original equation.Replace p with .11 = Simplify.The solution is .HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Use a Reciprocal to Solve an EquationSolve _ 2 5 x = _ 615 .2_5 x = _ 6152_5 x = ( 6 _15)x = or Simplify.Check Your ProgressSolve.a. _ m 9 = 4 b. _ 3 8 x = _ 3 4Write the equation.Multiply each side by theof 2_ 5 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.114 Math Connects, Course 2

5–7 Dividing Fractions and Mixed NumbersMAIN IDEA• Divide fractions andmixed numbers.KEY CONCEPTDivision by a FractionTo divide by a fraction,multiply by itsmultiplicative inverseor reciprocal.WRITE ITWill the quotient7 1_6 ÷ 3 2_3be a fractionless than 1 or greaterthan 1? Explain.EXAMPLE Divide by a FractionFind _ 2 3 ÷ _ 4 . Write in simplest form.92_3 ÷ 4_9 = 2_ · Multiply by the reciprocal4_3 9 .= 21_31· 93_42Divide out common factors.= or Multiply and simplify.EXAMPLE Divide by Mixed NumbersFind _ 5 6 ÷ 2 _ 1 . Write in simplest form.2Estimate 1 ÷ _ 5 = 1 × or2_2 55_6 ÷ 2 1_2 = _ 5 6 ÷ Rename 2 1_ 2fraction.as anCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= 5 _6 · Multiply by the reciprocal of 5 _2 .= Divide out common factors.=Check Your Progressa. _ 6 7 ÷ 2_5Multiply. The quotient is close tothe estimate.Divide. Write in simplest form.b. _ 3 8 ÷ 2 1_2Math Connects, Course 2 115

5–7EXAMPLEFACTORY A bottling machine needs to be restocked withnew lids every 2 _ 3 4 hours. If the machine runs 19 _ 1 4 hours,how many times will it have to be restocked with lids?19 1_4 ÷ 2 3 _4 = ÷ Rename the mixed numbers asimproper fractions.= _ 774 · _ 411= 777_41· 41_111Multiply by theof 11_ , which is4_4 11 .Divide out common factors.= or Multiply.So, the machine will need to restockedtimes.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress FURNITURE A rectangular tableis 5 _ 5 6 feet long. If the area of the table is 20 _ 5 square feet, how12wide is the table?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.116 Math Connects, Course 2

C H A P T E R5 BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 5 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 5, go to:glencoe.comYou can use your completedVocabulary Builder(page 103) to help yousolve the puzzle.5-1Estimating with FractionsEstimate.1. 8 2_3 + 7 1_42. 11 _ 7 8 ÷ 3 _ 5 65-2Adding and Subtracting FractionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Add or subtract. Write in simplest form.3. _ 7 8 + _ 3 85-34. _ 5 6 - 1_3Adding and Subtracting Mixed NumbersAdd or subtract. Write in simplest form.6. 3 _ 7 8 + 6 1_48. 8 _ 3 7 - 4 _ 5 77. 7 1_6 + 2 _ 5129. 9 2_9 - 1 2_35. 1_5 + _ 3 4Math Connects, Course 2 117

Chapter 5 BRINGING IT ALL TOGETHER5-4Problem-Solving Investigation: Eliminate Possibilities10. READING Joel read _ 5 of a novel. If the novel has 600 pages, is8250, 300, or 375 a reasonable number of pages that Joel has read?5-5Multiplying Fractions and Mixed NumbersMultiply. Write in simplest form.11. 2_7 × 4 1_513. 5 1_6 × 2_512. 1_6 × _ 3 414. _ 5 8 × 4_55-6Algebra: Solving EquationsFind the multiplicative inverse of each number.15. 3 _5Solve each equation.18. 1_3 a = _ 5 65-716. 1 1_219. -4 = k _3Dividing Fractions and Mixed NumbersDivide. Write in simplest form.20. 1_4 ÷ 2_322. 6 ÷ 1 1_321. _ 7 8 ÷ 2_323. 5 _ 3 4 ÷ 2 1_217. 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.118 Math Connects, Course 2

C H A P T E R5ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 5.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 5 Practice Test onpage 275 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 5 Study Guide and Reviewon pages 271–274 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 5 Practice Test onpage 275 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 5 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 5 Study Guide and Review onpages 271–274 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 5 Practice Test onpage 275 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 119

C H A P T E R6Ratios and Proportions®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of notebook paper.Fold lengthwiseto the holes.Cut along the top lineand then make equalcuts to form 7 tabs.Label the majortopics as shown. NOTE-TAKING TIP: When you take notes, it maybe helpful to include an example for each term orconcept learned.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.120 Math Connects, Course 2

C H A P T E R6BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 6.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecross productsequivalent ratiosgramCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.kilogramlitermetermetric systemproportionproportionalChapter 6rateMath Connects, Course 2 121

Chapter 6 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleratioscalescale drawingscale factorscale modelslopeunit rateunit ratioCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.122 Math Connects, Course 2

6–1RatiosMAIN IDEA• Write ratios asfractions in simplestform and determinewhether two ratios areequivalent.BUILD YOUR VOCABULARY (pages 121–122)Ais a comparison of two quantities by division.Ratios that express therelationship between twoquantities are equivalent ratios.EXAMPLE Write Ratios in Simplest FormAPPLES Mr. Gale bought a basketof apples. Using the table, write aratio comparing the Red Deliciousapples to the Granny Smith applesas a fraction in simplest form.10_Red Delicious 30_9 = 30 orGranny Smith 93Mr. Gale’s Apples12 Fuji9 Granny Smith30 Red DeliciousThe ratio of Red Delicious apples to Granny Smith applesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITRecord a term or conceptfrom Lesson 6–1 underthe Ratios tab and writea definition along withan example to the rightof the definition. is .EXAMPLE Identify Equivalent RatiosDetermine whether the ratios 12 onions to 15 potatoesand 32 onions to 40 potatoes are equivalent.12 onions : 15 potatoes = __ 12 ÷ 315 ÷ 3 or32 onions : 40 potatoes = __ 32 ÷ 840 ÷ 8 orThe ratios simplify to the same fraction. They are. Math Connects, Course 2 123

6–1Check Your Progressa. FLOWERS A garden has 18 roses and 24 tulips. Write aratio comparing roses to tulips as a fraction in simplest form.b. Determine whether the ratios 3 cups vinegar to 8 cups waterand 5 cups vinegar to 12 cups water are equivalent.REMEMBER ITRatios such as120 :1,800 can also bewritten in simplestform as 1:15.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEPOOLS It is recommended that no more than one personbe allowed into the shallow end of an outdoor publicpool for every 15 square feet of surface area. If a localpool’s shallow end has a surface area of 1,800 squarefeet, are the lifeguards correct to allow 120 people intothat part of the pool?Recommended Ratio1:15 = persons per square feetActual Ratio120:1,800 = _ 120 or persons per square feet1,800Since the ratios simplify to the same fraction, they are. The lifeguards are correct.Check Your Progress SCHOOL A district claims thatthey have 1 teacher for every 15 students. If they actually have2,700 students and 135 teachers, is their claim correct?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.124 Math Connects, Course 2

6–2 RatesMAIN IDEA• Determine unit rates.BUILD YOUR VOCABULARY (pages 121–122)A ratio thattwo quantities with differentkinds of units is called a rate.When a rate is simplified so that it has aof 1 unit, it is called a unit rate.®ORGANIZE ITUnder the rate tab, takenotes on rate and unitrate. Be sure to includeexamples.EXAMPLES Find Unit RatesREADING Julia read 52 pages in 2 hours. What is theaverage number of pages she read per hour?Write the rate as a fraction. Then find an equivalent rate with adenominator of 1.52 pages in 2 hours =__ 52 pages2 hoursWrite the rate as afraction.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. ==52 pages ÷___2 hours ÷pages__hoursDivide thenumerator anddenominator by .Simplify.SODA Find the unit price per can if it costs $3 for 6 cansof soda. Round to the nearest hundredth if necessary.$3 for 6 cans = __ $36 cans= __ $3 ÷ 66 cans ÷ 6Write the rate as a fraction.Divide the numerator and thedenominator by 6.= ___ Simplify.Math Connects, Course 2 125

6–2REMEMBER ITThe word rate isoften understood tomean unit rate.Check Your Progress Find each unit rate.a. 16 laps in 4 minutes b. $3 for one dozen cookiesEXAMPLE Compare Using Unit RatesTEST EXAMPLE The costs of 4 different sizes of orangejuice are shown in the table. Which container costs theleast per ounce?AmountTotal Cost16 oz $1.2832 oz $1.9264 oz $2.5696 oz $3.36A 96-oz containerB 64-oz containerC 32-oz containerD 16-oz containerRead the ItemFind the unit price, or the cost per ounce of each size of orangejuice. Divide the price by the number of ounces.Solve the Item$1.28 ÷ ounces = per ounce.$1.92 ÷ ounces = per ounce.$2.56 ÷ ounces = per ounce.$3.36 ÷ ounces = per ounce.The-ounce container of orange juice costs the least perounce. The answer is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.126 Math Connects, Course 2

6–2Check Your ProgressMULTIPLE CHOICE The costsof different sizes of bottles oflaundry detergent are shownbelow. Which bottle costs theleast per ounce?F 96-oz containerG 64-oz containerH 32-oz containerJ 16-oz containerAmount Total Cost16 oz $3.1232 oz $5.0464 oz $7.0496 oz $11.52EXAMPLE Use a Unit RateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:POTATOES An assistant cook peeled 18 potatoes in6 minutes. At this rate, how many potatoes can hepeel in 50 minutes?Find the unit rate.18 potatoes in 6 minutes = __ 18 ÷ 66 ÷ 6 = _ 3 1The unit rate is potatoes per minute.__ 3 potatoes· 50 min = potatoes1 minHe can peelpotatoes in 50 minutes.Check Your Progress Sarah can paint 21 beads in7 minutes. At this rate, how many beads can she paint inone hour?Math Connects, Course 2 127

6–3A Plan for Problem SolvingMAIN IDEA• Identify rate of changeand slope using tablesand graphs.BUILD YOUR VOCABULARY (pages 121–122)A rate of change is a rate that describes how one quantitychanges in relation to another and is usually expressed as a.EXAMPLE Find Rate of Change from a TableThe table shows the number of miles a car drove on atrip. Use the information to find the approximate rate ofchange.+ 65 + 65 +Distance (miles) 65 130 195 260Time (hours) 1 2 3 4+ 1 + 1 + 1WRITE ITExplain how rate ofchange is similar to unitrates.____change in distance= _change in timeSo, the rate was 65 miles per hour.The distance increasedmiles for every hour.Check Your Progress The table shows the number of milesa car drove on a trip. Use the information to find the rate ofchange.Distance (miles) 44 88 132 176Fuel (gallons) 2 4 6 8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.128 Math Connects, Course 2

6–3BUILD YOUR VOCABULARY (pages 121–122)The constant rate of change in y with respect to theconstant change inis called the slope of a line.EXAMPLE Find Rate of Change from a Graph®ORGANIZE ITUnder the rate ofchange and slope tab,take notes on how tofind the slope of a line. GRAPH THE DATA Find the slope of the line. Explainwhat the slope represents.Graph the points and connect themwith a line.Hours Amount Earned3 $456 $909 $135Pick two points on the line, suchas (3, 45) and (6, 90), to find theslope.change in yslope = __change in xAmount Earned (dollars)Earnings150140y130120110100908070605040302010 x03 6 9HoursCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.=90 -___6 -= 45 _3 orThe slope ishour.Check Your Progress Thetable shows the cost of renting abicycle. Graph the data. Find theslope of the line. Explain whatthe slope represents.Cost ($)40322416and represents the amount earned perHours Cost2 $84 $166 $24801 2 3 4 5 6 7 8 9HoursMath Connects, Course 2 129

6–4Measurement: Changing Customary UnitsMAIN IDEA• Change units in thecustomary system.BUILD YOUR VOCABULARY (pages 121–122)A unit ratio is a ratio in which the denominator isunit.EXAMPLES Convert Larger Units to Smaller UnitsREMEMBER ITYou multiply tochange from largerunits of measure becauseit takes more smallerunits than larger units tomeasure an object.Convert 2 miles into feet.Since 1 mile = 5,280 feet, the unit ratio is .5,280 ft2 mi = 2 mi ·__1 mi5,280 ft= 2 mi ·__1 mi__5,280 ftMultiply by .1 miDivide out common units.= ft or 10,560 ft Multiply.So, 2 miles =feet.REVIEW ITExplain how estimatingcan help you solve aproblem. (Lesson 6-1)ELEVATOR The elevator in an office building has aweight limit posted of one and a half tons. How manypounds can the elevator safely hold?1 1_2 t = 1 1_ t · Multiply by2since there arepounds in 1 ton.= 1 1_ · 2,000 lb or 3,000 lb Multiply.2So, the elevator can safely holdpounds.Check Your Progress Complete.a. 8 yd = ft b. 4 1_2 T = lbCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.130 Math Connects, Course 2

6–4EXAMPLES Convert Smaller Units to Larger UnitsConvert 11 cups into pints._Since 1 pint = 2 cups, the unit ratio is 2 c , and its1 ptreciprocal is .11 c = 11 c ·_1 pt2 c= 11 c ·_1 pt2 cMultiply by .Divide out common units.= 11 ·= 11_2 pt Multiplying 11 by 1_ is the same2as dividing 11 by 2.= ptSo, 11 cups =pints.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.SOCCER Tracy kicked a soccer ball 1,000 inches. Howmany feet did she kick the ball?Since 1 foot = 12 inches, multiply bycommon units.1 ft1,000 in. = 1,000 in. ·_12 in.= 1,000 in. · ft= _ 1000 ft or ft12So, Tracy kicked the soccer ball .. Then divide outMath Connects, Course 2 131

6–4Check Your Progress Complete.a. 21 qt = gal b. 78 oz = lbEXAMPLELEMONADE Paul made 6 pints of lemonade and poured itinto 10 glasses equally. How many cups of lemonade dideach glass contain?Begin by converting 6 pints to cups.6 pt = 6 pt · _ 1 pt= 6 · 2 cups or cupsFind the unit rate which gives the number of cups per glass.HOMEWORKASSIGNMENTPage(s):Exercises:__ 12 cups10 glasses = _ 6 or cups per glass5Check Your Progress CANDY Tom has 3 pounds of candyhe plans to divide evenly among himself and his 3 best friends.How many ounces of candy will each of them get?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.132 Math Connects, Course 2

6–5 Measurement: Changing Metric UnitsMAIN IDEA• Change metric units oflength, capacity, andmass.BUILD YOUR VOCABULARY (pages 121–122)The metric system is asystem of measures.The meter is the base unit of .The liter is the base unit of .The gram measures .The base unit of mass in the metric system is the.EXAMPLES Convert Units in the Metric SystemComplete 7.2 m = mm.To convert from meters to millimeters,Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITUnder the metric unitstab, take notes onhow to change metricunits, include examplesinvolving length,capacity, and mass. by .7.2 × =So, 7.2 m =mm.Complete 40 cm = m.To convert from centimeters to meters, by .40 ÷ =So, 40 cm = m.Math Connects, Course 2 133

6–5Check Your Progress Complete.a. 7.5 m = cm b. 3,400 mm = mEXAMPLEWRITE ITExplain how you canmultiply a number by apower of ten.FARMS A bucket holds 12.8 liters of water. Find thecapacity of the bucket in milliliters.You are converting fromto milliliters. Since thebucket holds 12.8 liters, use the relationship 1 L =mL.1 L = 1,000 mL Write the relationship.× 1 L = 12.8 × 1,000 mL Multiply each side by 12.8since you have 12.8 liters.12.8 L = mL To multiply 12.8 by 1,000,move the decimal pointplaces to the right.HOMEWORKASSIGNMENTPage(s):Exercises:So, the capacity of the bucket in milliliters isCheck Your Progress BOOKS A box of textbooks hasa mass of 32,850 grams. What is the mass of the box inkilograms?mL.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.134 Math Connects, Course 2

6–5EXAMPLES Convert Between Measurement SystemsConvert 7.13 miles to kilometers. Round to the nearesthundredth if necessary.Use the relationship 1≈ 1.61 kilometers.1 mi ≈ km Write the relationship.7.13 × 1 mi ≈ 7.13 × km Multiply each side bysince you have 7.13 mi.7.13 mi ≈ km Simplify.So, 7.13 miles is approximatelykilometers.Convert 925.48 grams to pounds. Round to the nearesthundredth if necessary.Since 1 pound ≈grams, the unit ratio is____ 1 lb453.6 g .1 lb925.48g ≈ g · . Multiply by .453.6 gCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.≈__ 925.48 lbor lb Simplify.453.6So, 925.48 grams is approximatelypounds.Check Your Progress Complete. Round to the nearesthundredth if necessary.a. 8.15 gal = L b. 5.75 m = ydMath Connects, Course 2 135

6–1 6–6Algebra: Solving ProportionsMAIN IDEA• Solve proportions.BUILD YOUR VOCABULARY (pages 121–122)Two quantities are proportional if they have arate or ratio.A proportion is an equation stating that two ratios or ratesare .In a proportion, a cross product is theofthe numerator of one ratio and the denominator of theother ratio.KEY CONCEPTProportion A proportionis an equation statingthat two ratios areequivalent.EXAMPLE Identify Proportional RelationshipsMATH Before dinner, Mohammed solved 8 mathproblems in 12 minutes. After dinner, he solved2 problems in 3 minutes. Is the number of problemshe solved proportional to the time?To identify proportional relationships, you can compare unitrates or compare ratios by comparing cross products. Let’scompare ratios by comparing .problemsminutes8_12 2_38 · 3 = · 224 = 24problemsminutesSince the cross products are , the number ofproblems solved is proportional to the time.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.136 Math Connects, Course 2

6–6Check Your Progress Determine if the quantities $30for 12 gallons of gasoline and $10 for 4 gallons of gasolineare proportional.EXAMPLES Solve a ProportionSolve _ 5 8 = _ 18x .5_8 = _ 18xWrite the proportion.5 · x = 8 · 18 Find the cross products.5x =Multiply._ 5x= _ 144 Divide each side by .®Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the proportionstab, take notes on howto solve a proportion.Include examples.HOMEWORKASSIGNMENTPage(s):Exercises: x =Solve _ 3.514 = _ 6 n ._ 3.5Simplify.14 = _n6 Write the proportion.3.5 · n = 14 · 6 Find the cross products.3.5n = Multiply.__ 3.5n 84= __ Divide each side by .n =Check Your Progressa. _ 915 = _ k18Simplify.Solve each proportion.b. _ 4.6w = 4_5Math Connects, Course 2 137

6–7 Problem-Solving Investigation:Draw a DiagramEXAMPLE Draw a DiagramMAIN IDEA• Solve problems bydrawing a diagram.ROCK CLIMBING A rock climber stops to rest at a ledge 90feet above the ground. If this represents 75% of the totalclimb, how high above the ground is the top of the rock?UNDERSTAND You know thatfeet is 75% of the totalheight. You need to find the total height.PLANSOLVEDraw a diagram showing the part alreadyclimbed.HOMEWORKASSIGNMENTPage(s):Exercises:You know that 75% ÷ 3 = 25%. If 75% of thetotal height is 90 feet, then 25% of the totalheight would be 90 ÷ 3, or 30, feet. You knowthat 75% + 25% = , so 90 feet + 30feet = 120 feet, which is the height of the topof the rock.CHECK Since 75%, or 0.75, of the total height is 90feet, and 90 ÷ 120 =checks., the solutionCheck Your Progress INVENTORY A retail store hastaken inventory of 400 items. If this represents 80% of the totalitems in the store, what is the total number of items in thestore?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.138 Math Connects, Course 2

6–8Scale DrawingsMAIN IDEA• Solve problemsinvolving scaledrawings.BUILD YOUR VOCABULARY (pages 121–122)Scale drawings and scale models are used to representobjects that are too or too to bedrawn at actual size.The scale gives the ratio that compares theof the drawing to the real object.EXAMPLE Use a Map Scale®MAPS What is the actualdistance between Portlandand Olympia?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the scale tab,explain how to solve aproblem involving scaledrawings. Be sure toinclude an example. Step 1 Use a ruler to find themap distance betweenthe two cities. Themap distance is about.Step 2 Write and solve a proportion using the scale. Letd represent the actual distance between the cities.mapactual3___ 8 inch1.69 inchesmap= __23 mi d miactual3_ × d = 23 × 1.69 Cross products.80.375d = 3.887d =The distance between the cities is about Multiply. Write 3 _8as a decimal.Divide both sidesby 0.375.kilometers.Math Connects, Course 2 139

6–8Check Your Progress MAPS On a map of California,the distance between San Diego and Bakersfield is about11 2_ centimeters. What is the actual distance if the scale is51 centimeter = 30 kilometers?WRITE ITExplain why these twoscales are equivalentscales:1_ inch = 4 miles21 inch = 8 milesEXAMPLE Use a Blueprint ScaleARCHITECTURE On the blueprintof a new house, each square hasa side length of _ 1 inch. If the length4 of a bedroom on the blueprint is1 _ 1 inches, what is the actual length2of the room?Write and solve a proportion.Scale Length of Roomblueprintactual1_4 inch___ = ___t feet blueprintactual1_ · t = Cross products41_4 t = _ 154t =The length of the room is .Multiply.Simplify.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.140 Math Connects, Course 2

6–8Check Your Progress On a blueprint of a new house,each square has a side length of 1_ inch. If the width of the4kitchen on the blueprint is 2 inches, what is the actual widthof the room? EXAMPLE Find a Scale FactorFind the scale factor of a blueprint if the scale is1_ inch = 3 feet.21___ 2 inch 1_3 feet =___ 2 inchConvert 3 feet to .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:1_2 inch= ·__36 inchesMultiply byto eliminatethe fraction in the numerator.= Divide out the common units.The scale factor is. That is, each measure on theblueprint is the measure.Check Your Progress Find the scale factor of a blueprint ifthe scale is 1 inch = 4 feet.Math Connects, Course 2 141

6–9 Fractions, Decimals, and PercentsEXAMPLES Percents as FractionsMAIN IDEA• Write percents asfractions and decimalsand vice versa.NUTRITION In a recent consumer poll, 41.8% of thepeople surveyed said they gained nutrition knowledgefrom family and friends. What fraction is this? Write insimplest form.41.8% = _ 41.8Write a fraction with a100denominator of 100.= _ 41.8100 · Multiply to eliminate thedecimal in the numerator.= or Simplify.®ORGANIZE ITUnder the Fractions,Decimals, and Percentstab, take notes onwriting percents asfractions and fractionsas percents. Includeexamples. Write 12 _ 1 % as a fraction in simplest form.212 1_ 12 1_2 % = _ 2Write a fraction.100= 12 1_ ÷ 100 Divide.2= ÷ 100 Write 12 1_ as an improper fraction.2= × Multiply by the reciprocal of 100.= or Simplify.Check Your Progressa. ELECTION In a recent election, 64.8% of registered votersactually voted. What fraction is this? Write in simplest form.b. Write 62 1_ % as a fraction in simplest form.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.142 Math Connects, Course 2

6–9KEY CONCEPTSCommon Fraction/Decimal/PercentEquivalents1_3 = 0. − 3 = 33 1_ 3 %2_3 = 0. − 6 = 66 2_ 3 %1_8 = 0.125 = 12 1_ 2 %3_8 = 0.375 = 37 1_ 2 %5_8 = 0.625 = 62 1_ 2 %7_8 = 0.875 = 87 1_ 2 %EXAMPLES Fractions as PercentsPRODUCE In one shipment of fruit to a grocery store,5 out of 8 bananas were still green. Find this amountas a percent.5_8 = n_100Write a proportion.500 = 8n Find the cross products._ 500=8n_ Divide each side by .So,= n Simplify.5_ = 621_8 2 % or .5_Write as a percent. Round to the nearest hundredth12if necessary.5_12 = n_100Write a proportion.= Find the cross products.500 12 ENTER 41.66666667 Use a calculator.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:So, _ 5 is about .12Write _ 3 as a percent. Round to the nearest hundredth.73_7 = 0.4285714… Write _ 3 as a decimal.7= by 100 and add the .Check Your Progress Write each fraction as a percent.Round to the nearest hundredth.a. _ 1325b. 11_15Math Connects, Course 2 143

C H A P T E R6BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 6 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 6, go to:glencoe.comYou can use your completedVocabulary Builder(pages 121–122) to help yousolve the puzzle.6-1RatiosState whether each sentence is true or false. If false, replacethe underlined word to make it a true sentence.1. When you simplify a ratio, write a fraction as a mixed number.2. To write a ratio comparing measures, both quantities shouldhave the same unit of measure.Write each ratio as a fraction in simplest form.3. 63 :7 4. 15: 546-2RatesComplete.5. A is a ratio that compares two quantities withdifferent kinds of units.Write each ratio as a fraction in simplest form.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. 36 inches: 48 inches 7. 15 minutes to 3 hours144 Math Connects, Course 2

Chapter 6 BRINGING IT ALL TOGETHER6-3Rate of Change and Slope8. The table shows Amanda’s running time during a 5-mile race.Graph the data. Find the slope of the line. Explain what the sloperepresents.40Distance(miles)Time(minutes)1 62 123 184 245 30Time (min)322416801 2 3 4 5 6 7 8 9Distance (mi)6-4Measurement: Changing Customary UnitsComplete.9. 3 _ 3 pt = c410. 90 ft = yd 11. 156 oz = lbCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6-5Measurement: Changing Metric UnitsComplete.12. 4.3 cm = mm 13. 42.7 g = mg6-6Algebra: Solving ProportionsComplete each sentence.14. The cross products of a are equal.15. If you know parts of a proportion, you can solve forthe fourth part byand thenboth sides by the coefficient of the unknown.Solve each proportion.16. _ 15n = _ 3 817. _ 620 = _ x8018. _ b16 = _ 348Math Connects, Course 2 145

Chapter 6 BRINGING IT ALL TOGETHER6-7Problem-Solving Investigation: Draw a Diagram19. LADDERS A ladder leans against a wall. The top of theladder rests against the wall at a point 12 feet above theground. If this distance represents 80% of the height of thewall, how tall is the wall?6-8Scale DrawingsOn a map, the scale is _ 1 inch = 10 miles. For each map4distance, find the actual distance.20. 6 inches 21. 3 _8 inch22. 2 1_ inches 23. 1 inch26-9Fractions, Decimals, and PercentsComplete the table of equivalent fractions.24. 1_325. 3 _826. 1_8Fraction Decimal Percent37 1_2 %27. 0.875 87 1_2 %Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.146 Math Connects, Course 2

C H A P T E R6ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study are givenwith each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 6.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 6 Practice Test onpage 337 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 6 Study Guide and Reviewon pages 333–336 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 6 Practice Test onpage 337 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 6 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 6 Study Guide and Review onpages 333–336 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 6 Practice Test onpage 337 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 147

C H A P T E R7 Applying Percents®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" × 17" paper.Fold the paperin half lengthwise.Open and refold thepaper into fourths alongthe opposite axis.Trace along the foldlines and label eachsection with a lessontitle or number.NOTE-TAKING TIP: When you take notes, it isoften helpful to reflect on ways the conceptsapply to your daily life.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.148 Math Connects, Course 2

C H A P T E R7BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 7.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplediscountpercent equationCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.percent of changepercent of decreasepercent of increase(continued on the next page)Chapter 7Math Connects, Course 2 149

Chapter 7 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplepercent proportionprincipalsales taxsimple interestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.150 Math Connects, Course 2

7–1Percent of a NumberEXAMPLE Find the Percent of a NumberMAIN IDEA• Find the percent of anumber.Find 8% of 125.METHOD 1 Write the percent as a fraction.8% =8_100 or2_ of 125 =2_× 125 or25 25METHOD 2 Write the percent as a decimal.8% =8_100 or0.08 of 125 = 0.08 × 125 orSo, 8% of 125 is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITFinding the percentof a number means tomultiply.Check Your Progress Find 72% of 350.EXAMPLE Use Percents Greater than 100%Find 125% of 64.You can either write the percent as a. Let’s write the percent as a decimal.125% = _ 125100 =or as a1.25 of 64 = 1.25 × 64 orSo, 125% of 64 is .Math Connects, Course 2 151

7–1Check Your Progress Find 225% of 50.EXAMPLELANGUAGES The graph below shows that 30% of thepeople in a community speak Spanish as their firstlanguage. If a community has 800 people, how manypeople can be expected to speak Spanish as their firstlanguage?HOMEWORKASSIGNMENTPage(s):Exercises:To find 30% of 800, write the percent as a .Then multiply.30% of 800 = 30% · 800So, about= · 800= 240their first language.people in the community speak Spanish asCheck Your Progress SLEEP The average person sleeps33% of their adult life. If their adult life consists of 62 years,how many years does the average person spend sleeping?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.152 Math Connects, Course 2

7–2The Percent ProportionMAIN IDEA• Solve problems usingthe percent proportion.BUILD YOUR VOCABULARY (pages 149–150)A percent proportion compares of a quantity tothe whole quantity, called the , using a percent.KEY CONCEPTPercent Proportion Thepercent proportionis __ partwhole = __ percent100 .EXAMPLE Find the PercentWhat percent of 24 is 18?18 is the part, and 24 is the whole. You need to find the percent.p_w = n_100=n_100Write the proportion.p = , w =18 · 100 = 24 · n Find the cross products.1,800 = 24n Simplify.= _ 24n24Divide each side by .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= n Simplify.So, of 24 is .EXAMPLE Find the PartWhat number is 30% of 150?30 is the percent and 150 is the base. You need to find the part.p_w = n_100Percent proportionp_150 = w = , n =p · 100 = 150 · 30100p =_ 100p100 = _ 4,500100Find the cross products.Simplify.Divide each side by 100.p =Simplify.So, 30% of is 45.Math Connects, Course 2 153

7–2EXAMPLE Find the Base12 is 80% of what number?12 is the part and 80 is the percent. You need to find the base.p_w = n_100Percent proportion_ 12w = a = , n = 80.= w · 80 Find the cross products.WRITE ITWrite an example ofa real-world percentproblem.1,200 = Simplify._ 1,2008= _ 80w80= wDivide each side by .So, 12 is 80% of 15.Check Your Progressa. What percent of 80 is 28?HOMEWORKASSIGNMENTPage(s):Exercises:b. What number is 65% of 180?c. 36 is 40% of what number?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.154 Math Connects, Course 2

7–3 Percent and EstimationEXAMPLEMAIN IDEA• Estimate percents byusing fractions anddecimals.CONCERTS A town sold 407 tickets to a chamber musicconcert in the town square. Of the tickets sold, 61% werediscounted for senior citizens. About how many seniorcitizens bought tickets for the concert?You need to estimate 61% of 407.61% is about 60%, and 407 is about 400.61% of 407 ≈ · 400 61% ≈ 3 _5≈ 240Multiply.So, aboutsenior citizens bought tickets.Check Your Progress TAXES Michelle discovered that27% of her paycheck was deducted for taxes. If her paycheckbefore taxes was $590, about how much was deducted for taxes?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITRecord the main ideas,and give examples aboutpercent and estimation inthe section for Lesson 7-3of your Foldable.®EXAMPLECOINS Melinda calculated that 40% of the coins in hercoin collection were minted before 1964. If there are715 coins in her collection, about how many of themwere minted before 1964?You can use a fraction or 10% of a number to estimate. Let’s use10% of a number.Step 1 Find 10% of the number.715 is about .10% of 700 = 0.1 · 700=(continued on the next page)Math Connects, Course 2 155

7–3Step 2 Multiply.40% of 700 is 4 · 10% of 700.4 × 70 =So, about coins were minted before 1964.Check Your Progress SAVINGS Suki saves 70% of hermonthly allowance. If her monthly allowance is $58, about howmuch does she save?EXAMPLES Percents Greater Than 100 or Less Than 1REMEMBER ITTo estimate thepercent of a number,round the percent,round the number, orround both.Estimate 173% of 60.173% is about 175%.175% of 60 = (100% of 60) + (75% of 60)= (1 · 60) + ( 3 _4 · 60 )HOMEWORKASSIGNMENTPage(s):Exercises:= 60 + 45 orSo, 173% of 60 is about .Estimate _ 1 % of 898.31_ % is one third of 1%. 898 is about 900.31% of 900 = 0.01 · 900 Write 1% as .= 9 Multiply.One third of 9 is 1_3 · 9 or .So, 1_ % of 898 is about .3Check Your Progress Estimate.a. 142% of 80 b. 1_ % of 1975Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.156 Math Connects, Course 2

7–4 Algebra: The Percent EquationMAIN IDEA• Solve problems byusing the percentequation.BUILD YOUR VOCABULARY (pages 149–150)The equation = percent · is called thepercent equation.EXAMPLE Find the PartORGANIZE ITRecord the main ideas,and give examples aboutthe percent equation inthe section for Lesson 7-4of your Foldable.®What number is 46% of 200?46% or is the percent and is the whole.Let p represent the .part = percent · wholep = · 200 Write an equation.p = Multiply.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.So, 46% of 200 is .EXAMPLE Find the Percent26 is what percent of 32?Let n represent the percent.part = percent · whole= n · 32 Write an equation.= Divide each side by .= n Simplify.= n Write as a percent.So, 26 is of 32.Math Connects, Course 2 157

7–4EXAMPLE Find the Whole12 is 40% of what number?Let w represent the whole.part = percent · whole= · w Write an equation.__0.40 = __ wDivide each side by .= wSo, 12 is 40% of .WRITE ITName two ways apercent can be written inthe percent equation.Check Your Progressa. What number is 72% of 500?HOMEWORKASSIGNMENTPage(s):Exercises:b. 18 is what percent of 80?c. 36 is 90% of what number?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.158 Math Connects, Course 2

7–5 Problem-Solving Investigation:Determine Reasonable AnswersEXAMPLE Solve. Use the Reasonable Answer Strategy.MAIN IDEA• Solve problemsby determiningreasonable answers.FUNDRAISER A soccer team is having a candy sale toraise funds to buy new shirts. The team gets to keep 25%of the sales. Each candy bar costs $1.50, and the teamhas sold 510 bars so far. If the shirts cost a total of $175,should the team order the shirts yet? Explain.UNDERSTAND You know the shirts cost a total of $175 andthat each candy bar costs $1.50. You know thatthe team has soldbars so far and thatthey get to keep 25% of the sales. You need toknow if the team has enough money to orderthe shirts yet.PLANFind how much the team has earned so far.Round 510 to 500. Then findsales.of theirSOLVE $1.50 · 500 =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:CHECKFind 25% of $750.25% of 750 = 0.25 · 750=The team gets to keep. Since thisis more than the cost of the shirts, they shouldorder the shirts.Use a calculator to check that the actualresult is 191.25, so the answer is reasonable.Check Your Progress FIELD TRIP There are 392students in the seventh grade at Hamilton Middle School. If35% of the seventh grade will attend the class field trip, is itreasonable to say that about 170 students will attend the fieldtrip? Explain.Math Connects, Course 2 159

7–6 Percent of ChangeMAIN IDEA• Find the percent ofincrease or decrease.BUILD YOUR VOCABULARY (pages 149–150)A percent of change is a ratio that compares the change inquantity to theamount.If the original quantity is, the percent ofchange is called the percent of increase.If the original quantity is, the percent ofchange is called the percent of decrease.EXAMPLE Find Percent of IncreaseSHOPPING Last year a sweater sold for $56. This year thesame sweater sells for $60. Find the percent of changein the cost of the sweater. Round to the nearest wholepercent if necessary.Since the new price isthis is a percent of60 - or .percent of increase =_____amount of increase= __56than the original price,. The amount of increase isSubstitution= Simplify.= Write as a .The percent of is about .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.160 Math Connects, Course 2

7–6Check Your Progress DVDs Last year a DVD sold for$20. This year the same DVD sells for $24. Find the percentof change in the cost of the DVD. Round to the nearest wholepercent if necessary.EXAMPLE Find Percent of Decrease®ORGANIZE ITRecord the main ideas,and give examples aboutpercent of change in thesection for Lesson 7-6 ofyour Foldable.ATTENDANCE On the first day of school this year, 435students reported to Howard Middle School. Last yearon the first day, 460 students attended. Find the percentof change for the first day attendance. Round to thenearest whole percent if necessary.Since the new enrollment figure isthan the figure foryear, this is a percent ofof decrease is - 435 or students.. The amountCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:percent of decrease = ______original amount=__ 25Substitution= Simplify.= Write as a percent.The percent of in the enrollment is about .Check Your Progress ZOO At the beginning of thesummer season, the local zoo reported having 385 animals in itscare. At the beginning of last year’s summer season the zoo hadreported 400 animals. Find the percent of change in the numberof animals at the zoo. Round to the nearest whole percent ifnecessary.Math Connects, Course 2 161

7–7Sales Tax and DiscountMAIN IDEA• Solve problemsinvolving sales taxand discount.BUILD YOUR VOCABULARY (pages 149–150)Sales tax is anamount of money charged onitems that people .Discount is the amount by which the regularof anitem is .EXAMPLE Find the Total CostORGANIZE ITRecord the main ideas,and give examples aboutsales tax and discount inthe section for Lesson 7-7of your Foldable.®GOLF A set of golf balls sells for $20, and the sales tax is5.75%. What is the total cost?To find the total cost, you can add sales tax to the regular priceor add the percent of tax to 100%. Let’s add sales tax to theregular price.First, find thetax.5.75% of $20 = · 20= The sales tax is .Next, add the sales tax to the regular price.+ 20 =The cost of the set of golf balls is .Check Your Progress BOOKS A set of three paperbackbooks sells for $35 and the sales tax is 7%. What is the totalcost of the set?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.162 Math Connects, Course 2

7–7EXAMPLE Find the Sale PriceREMEMBER ITThe cost of an itemwith sales tax willalways be greater thanthe regular price. Thediscounted price of anitem is always less thanthe regular price.OUTERWEAR Whitney wants to buy a new coat that hasa regular price of $185. This weekend, the coat is on saleat a 33% discount. What is the sale price of the coat?METHOD 1First, find the amount of the d.33% of $185 = · $185 Write 33% as a decimal.= The discount is $61.05.So, the sale price is $185 - or .METHOD 2First, subtract the of discount from 100%.100% - =So, the sale price isof the regular price.67% of $185 = · 185 Write 67% as a decimal.= Use a calculator.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.So, the sale price of the coat is .Check Your Progress ELECTRONICS Alex wants to buya DVD player that has a regular price of $175. This weekend,the DVD player is on sale at a 20% discount. What is the saleprice of the DVD player?Math Connects, Course 2 163

7–7EXAMPLE Find the Percent of the DiscountWATCHES A sports watch is on sale for $60.20 after a 30%discount. What is the original price?First, find the percent paid.100% - 30% =Next, use the equation to find the .Wordsis 70% of what amount?VariableLet n represent the original price.Equation60.20 = 70% ·60.20 = · n Write 70% as a decimal.= n each side by 0.70.The original price of the sports watch is .HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress FURNITURE A rocking chair ison sale for $318.75 after a 15% discount. What is the originalprice?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.164 Math Connects, Course 2

7–8Simple InterestMAIN IDEA• Solve problemsinvolving simpleinterest.BUILD YOUR VOCABULARY (pages 149–150)Simple Interest is the amount or earned for the useof money.Principal is the amount ofdeposited or.EXAMPLES Find Interest EarnedSAVINGS Brandon found a bank offering a certificate ofdeposit that pays 4% simple interest. He has $1,500 toinvest. How much interest will he earn in each amountof time?3 yearsI = prtFormula for simple interestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITRecord the main ideas,and give examples aboutsimple interest in thesection for Lesson 7-8 ofyour Foldable.®I = · · Replace the variables.I =Simplify.Brandon will earn in interest in years.30 months30 months = = years Write the time as years.I = prtFormula for simple interestI = · · Replace the variables.I =Simplify.Brandon will earn in interest in 30 months.Math Connects, Course 2 165

7–8WRITE ITWhich is better: a higherpercentage of intereston your credit card or onyour savings account?Explain.Check Your Progressa. SAVINGS Cheryl opens a savings account that pays 5%simple interest. She deposits $600. How much interest willshe earn in 2 years?b. SAVINGS Micah opens a savings account that pays 4%simple interest. He deposits $2,000. How much interest willhe earn in 42 months?EXAMPLE Find Interest Paid on a LoanLOANS Laura borrowed $2,000 from her credit union tobuy a computer. The interest rate is 9% per year. Howmuch interest will she pay if it takes 8 months to repaythe loan?HOMEWORKASSIGNMENTPage(s):Exercises:I =I = 2,000 · 0.09 · 8 _12I =Formula for simple interestReplace p withSimplify., and t with .Laura will pay in interest in months., r withCheck Your Progress LOANS Juan borrowed $7,500 fromthe bank to purchase a used car. The interest rate is 15% peryear. How much interest will he pay if it takes 2 years to repaythe loan?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.166 Math Connects, Course 2

C H A P T E R7BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 7 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 7, go to:glencoe.comYou can use your completedVocabulary Builder(pages 149–150) to help yousolve the puzzle.7-1Percent of a NumberFind each number.1. What is 3% of 530? 2. Find 15% of $24.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3. Find 200% of 17. 4. What is 0.6% of 800?7-2The Percent Proportion5. In the formula p _w = n_and n is the .6. What number is 30% of 15?7. 32.5 is 65% of what number?, p is the , w is the ,100Math Connects, Course 2 167

Chapter 7 BRINGING IT ALL TOGETHER7-3Percent and EstimationWrite fraction equivalents in simplest form for the followingpercents.8. 20% 9. 40% 10. 60% 11. 80%12. 25% 13. 50% 14. 75% 15. 100%Estimate.16. 49% of 80 17. 78% of 2518. 153% of 10 19. 0.5% of 2007-4Algebra: The Percent EquationWrite an equation for each problem. Then solve.20. 40% of what number is 48? 21. 18 is what percent of 72?22. Find 80% of 90. 23. 12% of what number is 60?7-5Problem-Solving Investigation: Determine ReasonableAnswers24. TRAVEL The Winston family determined that lodgingaccounted for 48% of their total travel costs. If they spent$1,240 total during their trip, would about $560, $620, or$750 be a reasonable amount that they spent on lodging?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.168 Math Connects, Course 2

Chapter 7 BRINGING IT ALL TOGETHER7-6Percent of ChangeState whether each sentence is true or false. If false,replace the underlined word to make a true sentence.25. If the new amount is less than the original amount, then thereis a percent of increase.26. The amount of increase is the new amount minus the originalamount.Find the percent of change. Round to the nearest wholepercent. State whether the percent of change is an increaseor decrease.27. original: $48; new: $44.25 28. original: $157; new: $181Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.29. original: $17.48; new: $9.98Math Connects, Course 2 169

Chapter 7 BRINGING IT ALL TOGETHER7-7Sales Tax and DiscountFind the total cost or sale price to the nearest cent.30. $29.99 jeans; 15% discount 31. $6.25 lunch; 8.5% sales taxFind the percent of discount to the nearest percent.32. Pen: regular price, $9.95; sale price, $6.9533. Sweatshirt: regular price, $20; sale price, $15.957-8Simple InterestFind the interest earned to the nearest cent for eachprincipal, interest rate, and time.34. $15,000, 9%, 2 years, 4 months35. $250, 3.5%, 6 yearsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.170 Math Connects, Course 2

C H A P T E R7ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 7.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 7 Practice Test onpage 389 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 7 Study Guide and Reviewon pages 384–388 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 389 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 7 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 7 Study Guide and Review onpages 384–388 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 389 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 171

C H A P T E R8 Statistics: Analyzing Data®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with nine sheets of notebook paper.Fold 9 sheets of paperin half along the width.Cut a 1" tab along theleft edge throughone thickness.Glue the 1" tab down.Write the lesson numberand title on the front tab.Repeat Steps 2 and 3 forthe remaining sheets.Staple them togetheron the glued tabs toform a booklet.NOTE-TAKING TIP: When you take notes, it issometimes helpful to make a graph, diagram,picture, chart, or concept map that presents theinformation introduced in the lesson.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.172 Math Connects, Course 2

C H A P T E R8BUILD YOUR VOCABULARYChapter 8This is an alphabetical list of new vocabulary terms you will learn in Chapter 8.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleanalyzebar graphbiased sampleCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.clusterdatahistograminferencesleafline graphline plot(continued on the next page)Math Connects, Course 2 173

Chapter 8 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemeanmeasures of centraltendencymedianmodeoutlierpopulationrandom samplerangescatter plotstatisticsstemstem-and-leaf plotsurveyCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.unbiased sample174 Math Connects, Course 2

8–1Line PlotsMAIN IDEA• Display and analyzedata using a line plot.BUILD YOUR VOCABULARY (pages 173–174)Statistics deals with collecting, organizing, and interpretingdata.A line plot is a diagram that shows the data on a numberline.Data that is grouped closely together is called a cluster.Outliers are numbers that are quite separated from the restof the data in a data set.EXAMPLE Display Data Using a Line PlotPRESIDENTS The table below shows the ages of the U.S.presidents at the time of their inaugurations. Make aline plot of the data.Age at Inauguration57 51 54 56 61 61 49 49 55 52 57 64 50 51 6957 50 47 54 64 58 48 55 51 46 57 65 55 60 5461 52 54 62 68 54 56 42 43 46 51 55 56Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITWrite a set of data thatcould be displayed in aline plot. Under the labfor Lesson 8-1, displaythe data in a line plot.®Step 1 Draw a number line. Use a scale of 40 to 70 and aninterval of 5.Step 2 Place an × above the number that represents the ageof each U.S. president. Check Your ProgressSTUDY TIME The table at the rightshows the number of minutes eachstudent in a math class spent studyingthe night before the last math exam.Make a line plot of the data. Minutes Studying36 42 60 3570 48 55 3260 58 42 5538 45 60 50Math Connects, Course 2 175

8–1BUILD YOUR VOCABULARY (pages 173–174)The range is the difference between the greatest and leastnumbers in the data set. When you analyze data, you useobservations to describe and compare data.EXAMPLE Use a Plot to Analyze DataREMEMBER ITA line plot does notneed to start at 0, butyou cannot leave outnumbers on the numberline when there are nox’s above them.CLIMATE The line plot shows the number of inchesof precipitation that fell in several cities west of theMississippi River during a recent year. Identify anyclusters, gaps, and outliers, and find the range ofthe data. 5 10 15 20 25 30 35 40 45 50There are data clusters betweenand 13 inches andbetween 16 andinches. There are gaps:between 18 and ; between and 32.HOMEWORKASSIGNMENTPage(s):Exercises:Since and 50 are apart from the rest of the data,they could be outliers.The range is - or inches.Check Your Progress AGE The line plot below shows theages of students in an introductory computer course at the localcommunity college. Identify any clusters, gaps, and outliers,and find the range of the data. 15 20 25 30 35 40 45Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.176 Math Connects, Course 2

8–1 8–2 Measures of Central Tendency and RangeMAIN IDEA• Describe a set of datausing mean, median,mode, and range.BUILD YOUR VOCABULARY (pages 173–174)Measures of central tendency can be used to describe thecenter of the data.The mean of a set of data is the sum of the data divided bythe number of items in the data set.EXAMPLE Find the MeanANIMALS The table below shows the number ofspecies of animals found at 30 major zoos across theUnited States. Find the mean.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.mean =Number of Species inMajor U.S. Zoos300 400 283 400 175617 700 700 715 280800 290 350 133 400195 347 488 435 640232 350 300 300 400705 400 800 300 659Source: The World Almanac300 + 400 + + … +_______30The mean number of species of animals is .sum of datanumber ofdata itemsCheck Your Progress SLEEP The table below showsthe results of a survey of 15 middle school students concerningthe number of hours of sleep they typically get each night.Find the mean.Nightly Hours of Sleep7 8 6 7 89 5 6 7 78 6 7 8 8Math Connects, Course 2 177

8–2®ORGANIZE ITUnder the tab forLesson 8-2, define anddifferentiate betweenmean, median, andmode.BUILD YOUR VOCABULARY (pages 173–174)The median of a set of data is the middle number of theordered data, or the mean of the middle two numbers.The mode or modes of a set of data is the number ornumbers that occur most often.EXAMPLE Find the Mean, Median, and ModeOLYMPICS The table below shows the number of goldmedals won by each country participating in the 2002Winter Olympic games. Find the mean, median, andmode of the data.2002 Winter Olympics:Gold Medals Won12 6 4 3 010 6 4 2 311 2 3 4 21 1 0 2 21 0 0 0 0mean: sum of data divided by , ormedian: 13th number of the data, ormode: number appearing often, orCheck Your Progress PETS The table below shows thenumber of pets students in an art class at Green Hills MiddleSchool have at home. Find the mean, median, and mode ofthe data.Pets0 2 1 01 3 5 20 1 0 23 1 2 0Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.178 Math Connects, Course 2

8–2EXAMPLETEST EXAMPLE The average weight in pounds of severalbreeds of dogs is listed below.15, 45, 26, 55, 15, 30If the average weight of the Golden Retriever, 70pounds, is added to this list, which of the followingstatements would be true?A The mode would increase.B The median would decrease.C The median would increase.D The mean would decrease.Read the ItemYou are asked to identify which statement would be true if thedata valuewas added to the data set.Solve the ItemUse number sense to eliminate possibilities.The mode,, will remain unchanged since the new datavalue occurs only once. So, eliminate choice .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Since the new data value isthan each value inthe data set, neither the mean nor median will decrease. So,eliminate choices B and .Since 70 is greater than each value in the data set, the medianwill now . So, the answer is .Check Your Progress If the average weight of theChihuahua, 4 pounds, is added to the list above, which of thefollowing statements would be true?F The mean would decrease.G The mode would decrease.H The median would stay the same.J The mean would increase.Math Connects, Course 2 179

8–3 Stem-and-Leaf PlotsMAIN IDEA• Display and analyzedata in a stem-and-leafplot.BUILD YOUR VOCABULARY (pages 173–174)In a stem-and-leaf plot, the data are organized fromto .The digits of theplace value usually form theleaves and the next place-value digits form the stems.EXAMPLE Display Data in a Stem-and-Leaf PlotBASEBALL The table below shows the number of homeruns that Babe Ruth hit during his career from 1914 to1935. Make a stem-and-leaf plot of the data.®ORGANIZE ITUnder the tab forLesson 8-3, give anexample of a set ofdata for which a stemand-leafplot would beappropriate. Draw thestem-and-leaf plot.Home Runs0 54 25 464 59 47 413 35 60 342 41 54 611 22 4629 46 49Step 1 The digits in theplace value will formthe leaves and the remaining digits will form the. In these data, is the least value,and is the greatest. So, the ones digit willform the and the digit willform the stems.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.180 Math Connects, Course 2

8–3Step 2 List the stems 0 toin order from least to greatestin the Stem column. Write the leaves, thedigits of the home runs, to thecorresponding stems.of theStep 3 Order the leaves and write a key that explains how toread the stems and leavesStemLeaf0 0 2 3 4 61The tensdigits ofthe dataform thestems.23 4 51 1 6 6 6 7 956 0 2 5 = 25 home runsThe onesdigits ofthe dataform theleaves.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress BUSINESS The table showsthe number of hours several business men and women spentaboard an airplane. Make a stem-and-leaf plot of the data.Hours Aboard an Airplane4 18 0 23 12 7 935 14 6 11 21 19 615 26 9 0 13 22 10A key shows howthe digits are related.Math Connects, Course 2 181

8–3EXAMPLE Describe DataWRITE ITExplain how to find howmany items are on astem-and-leaf plot.FITNESS The stem-and-leaf plot below shows the numberof miles that Megan biked each day during July. Findthe range, median, and mode of the data.StemLeaf0 5 5 5 61 0 0 0 0 1 2 2 5 8 8 92 1 2 5 83 0 2 5 = 25 milesrange: greatest distance - least distance = -ormilesmedian: middle value, ormode: most frequent value, ormilesmilesCheck Your Progress SNOWFALL The stem-and-leaf plotbelow shows the number of inches of snow that fell in Hightownduring the month of January for the past 15 years. Find therange, median, and mode.StemLeaf0 1 3 5 7 91 0 0 0 2 4 4 7 82 2 6 1 2 = 12 inchesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.182 Math Connects, Course 2

8–3EXAMPLE Effects of OutliersANIMALS The averagelife span of severalanimal species is shownin the stem-and-leaf plot.Which measure of centraltendency is most affectedby the inclusion of theoutlier?Animals’ Life SpansStem Leaf0 3 4 6 81 0 0 2 2 2 5 5 6 82 0 0 0 0 234 0 1 0 = 10 yearsThe mode,, is not affected by the inclusion of the outlier,.Calculate the mean and median each without the ,40. Then calculate them including the outlier and compare.without the outliermean:___3 + 4 +…+ 22≈ 12.418including the outlier____ 3 + 4 +…+ 20 +≈ 13.8median:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:The mean increased by 13.8 - 12.4, or, while the medianincreased by 15 - 13.5, or . So, the is mostaffected by the inclusion of the outlier.Check Your ProgressTEST SCORES The testscores earned by a classof middle school mathstudents on a chapter testare shown. Which measureof central tendency is mostaffected by the inclusion ofthe outlier?Test ScoresStem Leaf5 867 5 6 7 98 0 0 1 2 2 5 5 6 6 79 0 2 3 3 3 4 4 67 5 = 75 pointsMath Connects, Course 2 183

8–4 Bar Graphs and HistogramsMAIN IDEA• Display and analyzedata using bar graphsand histograms.BUILD YOUR VOCABULARY (pages 173–174)A bar graph is one method ofdata byusing solid bars to represent quantities.EXAMPLE Display Data Using a Bar GraphTOURISM Make a bar graph to display the data in thetable below.®ORGANIZE ITUnder the tab forLesson 8-4, draw a sketchof a bar graph and ahistogram and describetheir similarities anddifferences.CountryVacation Days per YearItaly 42France 37Germany 35Brazil 34United Kingdom 28Canada 26Korea 25Japan 25United States 13Source: The World AlmanacStep 1 Draw and label the axes. Then choose aon the vertical axis so that it includes all of thevacation days per year.Step 2 Draw aNumber of Days5040302010to represent each category.ItalyFranceGermanyBrazilU.K.Canada0Vacation DaysCountryKoreaJapanU.S.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.184 Math Connects, Course 2

8–4Check Your Progress Runner MilesSPORTS The table shows the averagenumber of miles run each day duringtraining by members of the crosscountry track team. Make a bargraph to display the data.Bob 9Tamika 12David 14Anne 8Jonas 5Hana 10BUILD YOUR VOCABULARY (pages 173–174)A histogram is a special kind ofgraph that usesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITExplain when you woulduse a bar graph andwhen you would usea histogram.bars to represent the frequency of numerical data thathave been organized in .EXAMPLE Display Data Using a HistogramBASKETBALL The number of wins for 29 teams of abasketball league for a season have been organized intoa frequency table. Make a histogram of the data.Number of WinsFrequency11–20 321–30 431–40 441–50 1051–60 8(continued on the next page)Math Connects, Course 2 185

8–4Step 1 Draw and horizontal and axes.Add a .Step 2 Draw a bar to represent theinterval.of each Check Your Progress SPEED The speeds of cars on astretch of interstate are clocked by a police officer and havebeen organized into a frequency table. Make a histogramof the data.Speed (mph) Frequency50–59 260–69 1470–79 1880–89 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.186 Math Connects, Course 2

8–4EXAMPLES Analyze Data to Make InferencesDINING OUT The bar graph shows the number of timespeople dine out each month.# people1614121086420Eating Out0–1011–2021–3031–4041–5051–60# times per monthHow many people are represented in the histogram?Justify your answer.Find the sum of the heights of the bars in the histogram.5 + + + 15 + 7 + =What percent of people surveyed ate out more than 40times per month?_ 7 + 5= __50 50number of people who ate out morethan 40 timestotal number of people surveyed_ 12= Write the fraction as a decimal.50Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:0.24 = Write the decimal as a percent.So, 24% of the people surveyed ate out more than40 times per month.Check Your ProgressHOUSING The bar graph showsthe number of houses sold invarious price ranges.a. How many houses arerepresented in the histogram?b. What percent of houses were sold for more than $200,00Frequency4035302520151050100,001–150,000Housing Prices150,001–200,000200,001– 250,001–250,000 300,000Price ($)Math Connects, Course 2 187

8–5 Problem-Solving Investigation: Use a GraphEXAMPLE Solve Problems by Using a GraphMAIN IDEA• Solve problems byusing a graph.VCR SALES Based on the information in the graph, howmany VCRs would you expect to be sold in 2012?Millions Sold706050403020100VCR Sales00 01 02 03 04 05 06 07YearUNDERSTAND You know that the graph shows a rapiddownward trend. You need to determine howmany VCRs would be expected to be sold in2012.PLANLook at the trend of the graph. Predict thenumber of VCR sales in 2012.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVECHECKThe graph shows a rapidIf the trend continues, no VCRs will beexpected to be sold in 2012.The graph rapidly decreases. The answer isreasonable.VCRs would be sold in .trend. If it continued,Check Your Progress TEMPERATURE Refer to thegraph below. Suppose the trends continue. Predict the averagehigh temperature for the month of August.Miami Average Temperatures100908070Temperatures6050Average HighAverage LowCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.0JanFebMarAprMayJunMonths188 Math Connects, Course 2

8–6Using Graphs to PredictMAIN IDEA• Analyze line graphsand scatter plots tomake predictions andconclusions.BUILD YOUR VOCABULARY (pages 173–174)Line graphs can be useful in predictingeventswhen they show trends over .EXAMPLE Use a Line Graph to PredictCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITUnder the tab forLesson 8-6, includean example of a linegraph and explain howit can be used to makepredictions.TYPING The line graph shows the time it has takenEnrique to type a class paper so far. The paper is 600words long. Use the graph to predict the total time itwill take him to type his paper.By looking at the pattern inEnrique’s Typingthe graph, you can predict 700that it will take Enriqueaboutminutes totype his 600-word paper.Words Typed6005004003002001000 2 4 6 8 10 12 14 16Time (min)Check Your Progress TRAVEL During a recent roadtrip, Helen kept track of the number of miles traveled aftereach hour of travel time was completed. The table shows herinformation. Use the line graph to predict how far Helen willtravel in 12 hours of travel time. Math Connects, Course 2 189

8–6WRITE ITExplain how a line graphcan help you to make aprediction.BUILD YOUR VOCABULARY (pages 173–174)A scatter plot displays two sets of data on the same graphand are also useful in making .EXAMPLE Use a Scatter Plot to PredictPOLLUTION The scatter plot shows the number of daysthat a city failed to meet air quality standards from 2000to 2008. Use it to predict the number of days of bad airquality in 2014.By looking at the pattern, youcan predict that the number ofdays of bad air quality in 2014will be aboutdays.Number of Days with AQIValues Greater than 100Bad Air Quality Days180160140120100806040200’02 ’06 ’10 ’14YearHOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress GAS MILEAGE Use the scatterplot below to predict the gas mileage for a car weighing5500 pounds. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.190 Math Connects, Course 2

8–7 Using Data to PredictMAIN IDEA• Predict actions of alarger group by usinga sample.BUILD YOUR VOCABULARY (pages 173–174)A survey is designed to collect about a specificgroup of people, called the population.EXAMPLEORGANIZE ITUnder the tab for Lesson8-7, give examples aboutusing statistics to predict.®PETS The table shows theresults of a survey in whichpeople were asked whethertheir house pets watchtelevision. There are 540students at McCloskey MiddleSchool who own pets. Predicthow many of them would saytheir pets watch TV.Does your pet watchtelevision?ResponsePercentyes 38%no 60%don’t know 2%You can use the percent proportion and the survey results topredict the number of people who said their pets watch TV.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.part of thepopulationentirepopulationAboutp_w = n_100Percent proportion__ p= Survey results: 38% =100a =watch television.a =Cross productsSimplify.of the people surveyed said that their petsMath Connects, Course 2 191

8–7REVIEW ITSolve the proportion7_9 = x_27 .Check Your Progress VIDEO GAMES In a survey ofmiddle school students, 32% responded that playing videogames was their favorite after-school activity. Predict howmany of the 260 students surveyed said that playing videogames was their favorite after-school activity.EXAMPLESUMMER JOBS According to one survey, 25% of highschool students reported they would not get summerjobs. Predict how many of the 948 students at MohawkHigh School will not get summer jobs.You need to predict how many of theget summer jobs.students will notWordsWhat number is 25% of 948?VariableLet n represent the .HOMEWORKASSIGNMENTPage(s):Exercises:Equationn = · 948n = · 948 Write the equation.n =Multiply.So, you could predict that about of the students atMohawk High School will not get summer jobs.Check Your Progress SEASONS According to one survey,31% of adults consider spring to be their favorite season ofthe year. Predict how many of the 525 employees of a largecorporation would respond that spring is their favorite seasonof the year.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.192 Math Connects, Course 2

8–8Using Sampling to PredictMAIN IDEA• Predict the actions of alarger group by using asample.BUILD YOUR VOCABULARY (pages 173–174)A sample is representative of a larger population. Anunbiased sample is representative of the entire population.A simple random sample is the most common type ofunbiased sample.A biased sample occurs when one or more parts of thepopulation are favored over others. A convenience sampleincludes members of a population who are easily accessed.A voluntary response sample involves only those who wantto participate in sampling.EXAMPLE Determine Validity of ConclusionsDetermine whether the conclusion is valid. Justify youranswer.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A newspaper asks its readers to answer a poll aboutwhether or not an issue should be on the ballot in anupcoming election. 85% of the readers who respondedsaid that they wanted the issue on the ballot, so thenewspaper printed an article saying that 85% of peoplewant the issue on the ballot.The conclusion is. The population is restrictedto readers and it is a voluntary response sample and is. The results of a voluntary response sample do notnecessarily represent the entire .Math Connects, Course 2 193

8–8Check Your Progress Determine whether theconlusion is valid. Justify your answer.A coffee shop asks every tenth customer that comes inthe door to identify their favorite coffee drink. 45% of thecustomers surveyed said the mocha coffee is their favoritedrink. The manager of the store concluded that about half ofthe store’s customers like the mocha coffee.EXAMPLEVENDING MACHINES An office building managerinterviewed 60 of their employees to determine whetheror not a vending machine should be placed in the breakroom. 45 of the employees said yes and 15 said no. Ifthere are 255 employees in the building, predict howmany employees would like a vending machine in thebreak room.The sample is an unbiasedsample since employeeswere randomly selected. Thus, the sample is valid.HOMEWORKASSIGNMENTPage(s):Exercises:_ 45or % of the employees would like a vending machine60in the break room. So, find 75% of .0.75 × 255 = 75% of 255 = 0.75 255So, aboutthe break room.employees would like a vending machine inCheck Your Progress CLUBS A Spanish teacher istrying to determine if students would be interested in joininga Spanish club. She randomly asked 30 of her students. 18 ofthe students said yes and 12 said no. If the teacher has 105students in her Spanish classes, predict how many would liketo join a Spanish club.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.194 Math Connects, Course 2

8–9 Misleading StatisticsEXAMPLE Changing the Interval of GraphsMAIN IDEA• Recognize whenstatistics and graphsare misleading.BUSINESS The line graphs below show the last 10 weeksof sales for the Crumby Cookie Bakery.Sales ($)1,2001,000800600012Sales, Graph A34 5 6Week78910a. Do the graphs show the same data? If so, explain howthe graphs differ.Sales ($)1,025950875800012Sales, Graph B34 5 6Week78910The graphs show thedata. However, the graphsdiffer in that Graph has greater intervals and a greaterrange.b. Which graph makes it appear that the bakery’s salesdeclined only slightly?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Graph makes it appear that the sales declined onlyslightly even though both graphs show the same decline.Check Your Progress SOCCER The graphs show thenumber of wins by four different soccer teams. Do the graphsshow the same data? If so, explain how they differ. Math Connects, Course 2 195

8–9®ORGANIZE ITUnder the tab forLesson 8-9, explain howto recognize misleadinggraphs and statistics.EXAMPLE Misleading StatisticsGRADES Michael and Melissa both claim to be earninga C average, 70% to 79%, in their Latin class. One studentis wrong. Which one? Explain how he or she is using amisleading statistic.meanGrade (%)Michael:TestMichael MelissaMelissa:medianMichael:Melissa:1 80 882 76 833 73 754 70 705 40 606 25 657 10 62Michael is wrong. He is using thegrade rather than theaverage, is 70% or better.to describe his. Only Melissa’s mean, orHOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress RETAIL SALES Two differentgrocery stores each claim to have the lowest average prices.Use the table to explain their reasoning and determine whichstore really has the lowest average prices.Item Store A Store BMilk $1.29 $1.34Bread $1.99 $1.85Eggs $1.19 $1.09Soda $2.29 $2.99Coffee $7.99 $5.29Ice Cream $4.39 $4.19Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.196 Math Connects, Course 2

C H A P T E R8BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 8 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 8, go to:glencoe.comYou can use your completedVocabulary Builder(pages 173–174) to help yousolve the puzzle.8-1Line PlotsThe line plot shows prices for different running shoes.10 20 30 40 50 60 70 80 90 100Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1. What is the range of the prices?8-2Measures of Central Tendency and RangeFind the mean, median, and mode of each set of data.2. 2, 5, 5, 6, 8, 11, 12 3. 6, 5, 12, 34, 20, 178-3Stem-and-Leaf Plots4. The stem-and-leaf plot shows testscores for 13 students. Find the range,median, and mode of the data.Stem Leaf0 7 81 5 5 6 92 0 2 2 3 3 3 41 5 = 15Math Connects, Course 2 197

Chapter 8 BRINGING IT ALL TOGETHER8-4Bar Graphs and HistogramsWrite true or false for each statement. If the statement is false,replace the underlined words with words that will make thestatement true.5. A bar graph is used to compare data.6. A histogram shows categories on one of the axes.8-5Problem-Solving Investigation: Use a GraphThe graph shows the results of asurvey about favorite countriesstudents would like to visit.7. Which place was favored bymost students?8. Compare the number of studentsthat would like to visit Italy versusIreland.8-6Using Graphs To PredictRefer to the graph shown.9. Mark the City Zoo graph to show howto predict the attendance in 2005.10. If the trend continues, predict theattendance in 2005. Attendance (thousands)1210864City Zoo20’99 ’00 ’01 ’02 ’03 ’04 ’05Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Year198 Math Connects, Course 2

Chapter 8 BRINGING IT ALL TOGETHER8-7Using Data To Predict11. LUNCHES A survey of 7th graders 12. ZOO A survey of zoo visitors showedshowed that 44% bring their lunch that 28% chose the lion exhibit as theirto school. Predict how many offavorite. If 338 people visited today,the 450 7th graders bring theirpredict how many would choose the lionlunch to school.exhibit as their favorite.8-8Using Sampling To PredictDetermine whether each conclusion is valid. Justifyyour answer.13. A researcher randomly surveys ten employees from each department of a largecompany to determine the number of employees that buy their lunch in the cafeteria.Of these, 82% said they do buy their lunch in the cafeteria. The researcher concludesthat most of the employees do buy their lunch in the cafeteria.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14. Every tenth customer who purchases books from an online store is asked to take asurvey. The majority of those who replied said they would like more shipping options.As a result, the store adds more shipping options for their customers.8-9Misleading StatisticsThe table lists the number of wrong answers astudent had on her homework papers this year.15. Which measure of central tendency might sheuse to emphasize her good work?16. Which measure of central tendency best representsher work? Explain.Wrong Answers1 8 2 7 26 8 7 2 47 2 5 8 6Math Connects, Course 2 199

C H A P T E R8ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 8.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 8 Practice Test onpage 455 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 8 Study Guide and Reviewon pages 450–454 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 8 Practice Test onpage 455 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 8 Foldables.• Then complete the Chapter 8 Study Guide and Review onpages 450–454 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 8 Practice Test onpage 455 of your textbook.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature200 Math Connects, Course 2

C H A P T E R9 Probability®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 8 _ 1 " by 11" paper.2Stack 5 sheets ofpaper 3_ inch apart.4Roll up bottom edgesso that all tabs are thesame size.Chapter 9Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Crease and staplealong fold.Write the chapter titleon the front. Label eachtab with a lesson numberand title. Label the lasttab Vocabulary.NOTE-TAKING TIP: When taking notes, writinga paragraph that describes the concepts, thecomputational skills and the graphics will help youto understand the math in a lesson.Math Connects, Course 2 201

C H A P T E R9BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 9.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description of thesepages. Remember to add the textbook page number in the second column forreference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecombinationcomplementary events[KAHM-pluh-MEHNtuh-ree]composite eventsexperimentalprobability[ihk-SPEHR-uh-MEHN-tuhl]fair gameFundamental CountingPrincipleCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.202 Math Connects, Course 2

Chapter 9 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleindependent eventoutcomepermutation[PUHR-myu-TAYshuhn]probability[PRAH-buh-BIH-luhtee]Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.randomsample spacesimple eventtheoretical probability[thee-uh-REHT-uhkuhl]tree diagramMath Connects, Course 2 203

9–1Simple EventsMAIN IDEA• Find the probability ofa simple event.BUILD YOUR VOCABULARY (pages 202–203)An outcome is any possible .KEY CONCEPTA simple event is oneof outcomes.or a collectionProbability Theprobability of an eventis a ratio that comparesthe number of favorableoutcomes to the numberof possible outcomes.®On the tabfor Lesson 9–1, takenotes on how to findthe probability of simpleevents. Include examples.Outcomes occur at random if each outcome occurs byEXAMPLE Find Probability.If the spinner shown is spun once,what is the probability of its landing onan odd number?P(odd number) =____odd numbers possibletotal numbers possible4312=2_ Two numbers are odd: 1 and 3.= Simplify.The probability of spinning an odd number is 1_2 or .Check Your Progress What is the probability of rolling anumber less than three on a number cube marked with 1, 2, 3,4, 5, and 6 on its faces?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.204 Math Connects, Course 2

9–1REVIEW ITExplain how to subtract afraction from 1.EXAMPLEGAMES A game requires spinning the spinner shownin Example 1. If the number spun is greater than 3, theplayer wins. What is the probability of winning thegame?Let P(A) be the probability that the player will win.number of favorable outcomesP(A) = ______number of possible outcomes= 1_4The probability of winning the game is .BUILD YOUR VOCABULARY (pages 202–203)The sum of the probabilities of complementary eventsis 1 or 100%.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEGAMES What is the probability of not winning the gamedescribed in Example 2?P(A) + P(not A) = 1 Defi nition of complementary events- 1_41_ + P(not A) = 1 Replace P(A) with1_4 4 .P(not A) =- 1_4Subtract 1_ from each side.4The probability of not winning the game is 3 _4 .Check Your Progress A game requires spinning thespinner shown in Example 1. If the number spun is less than orequal to 2, the player wins.a. What is the probability of winning the game?b. What is the probability of not winning the game?Math Connects, Course 2 205

9–2 Sample SpacesMAIN IDEA• Find sample spaces andprobabilities.BUILD YOUR VOCABULARY (pages 202–203)The sample space is the set of alloutcomes.A tree diagram can be used to display the.EXAMPLE Find the Sample Space®ORGANIZE ITOn the tab for Lesson9–2, record what youlearn about samplespaces. Explain how tofind probability using atree diagram.CHILDREN A couple would like to have two children.Find the sample space of the children’s genders if havinga boy is equally likely as having a girl.Make a table that shows all of the possible outcomes.girlgirlboyboyboygirlCheck Your Progress CARS A dealer sells a car in red,black, or white. The car also can be 2-door or 4-door. Find thesample space for all possible cars available from this dealer.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.206 Math Connects, Course 2

9–2EXAMPLETEST EXAMPLE Amy was trying to decide what kind ofsandwich to make. She had two kinds of bread, wheatand sourdough. And she had three kinds of lunchmeat,ham, turkey, and roast beef. Which list shows all thepossible bread-lunchmeat combinations?ABOutcomeswheat hamsourdough turkeywheat turkeysourdough hamOutcomeswheat hamwheat turkeywheat roast beefCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.CDwheatwheatwheatsourdoughsourdoughsourdoughwheatsourdoughwheatsourdoughwheatsourdoughOutcomesOutcomeshamturkeyroast beefhamturkeyroast beefturkeyturkeyturkeyhamhamhamRead the ItemThere are two bread choices and three lunchmeat choices. Findall of the bread-lunchmeat combinations.(continued on the next page)Math Connects, Course 2 207

9–2WRITE ITSolve the ItemMake a tree diagram to show the sample space.In a probability gameusing two counters Aand B, what would theoutcome BA mean?WheatSourdoughHamTurkeyRoast BeefHamTurkeyRoast BeefThere are 6 different bread-lunchmeat combinations.The answer is .HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress MULTIPLE CHOICE A new carcan be ordered with exterior color choices of black, red, andwhite, and interior color choices of tan, gray, and blue. Whichlist shows the different cars that are possible?F OutcomesH OutcomesGblackredwhiteblackredwhiteblackredwhiteblackredwhiteblacktantantanOutcomesgraygraygraybluebluebluetangraybluegrayJblackredwhiteblackredwhiteblackredwhitetangraybluegraybluetanOutcomestangrayblueCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.208 Math Connects, Course 2

9–3 The Fundamental Counting PrincipleMAIN IDEA• Use multiplication tocount outcomes andfind probabilities.KEY CONCEPTThe FundamentalCounting Principle Ifevent M can occur in mways and is followed byevent N that can occur inn ways, then the event Mfollowed by N can occurin m × n ways.®Include thisconcept in your notes.BUILD YOUR VOCABULARY (pages 202–203)You can use the Fundamental Counting Principle to find thenumber of possible outcomes in a sample space.EXAMPLECLOTHING The table below shows the shirts, shorts, andshoes in Gerry’s wardrobe. How many possible outfits—one shirt, one pair of shorts, and one pair of shoes—canhe choose?Shirts Shorts Shoesred beige blackblue green brownwhiteyellowblueshirts × shorts × shoes = totalCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:There are× × =possible outfits that Gerry can choose.Check Your Progress SANDWICHES The table belowshows the types of bread, types of cheese, and types of meatthat are available to make a sandwich. How many possiblesandwiches can be made by selecting one type of bread, onetype of cheese, and one type of meat?Bread Cheese MeatWhite American TurkeyWheat Swiss HamRye Mozzarella Roast BeefMath Connects, Course 2 209

9–1 9–4PermutationsMAIN IDEA• Find the number ofpermutations of a setof objects and findprobabilities.BUILD YOUR VOCABULARY (pages 202–203)A permutation is an, or listing of objectsin whichis important.EXAMPLE Find a PermutationBOWLING A team of bowlers has five members, who bowlone at a time. In how many orders can they bowl?There areThere arechoices for the first bowler.choices for the second bowler.There areThere arechoices for the third bowler.choices for the fourth bowler.KEY CONCEPTFactorial The expressionn factorial (n!) is theproduct of all countingnumbers beginning withn and counting backwardto 1.5 · 4 · 3 · 2 · 1 =There arethe five bowlers.There ischoice that remains.possible arrangements, or permutations, ofCheck Your Progress TRACK AND FIELD A relay teamhas four members who run one at a time. In how many orderscan they run?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.210 Math Connects, Course 2

9–4EXAMPLE Find a Permutation®ORGANIZE ITOn the tab for Lesson9–4, record whatyou learn aboutpermutations.RAFFLE A school fair holds a raffle with 1 st , 2 nd , and3 rd prizes. Seven people enter the raffle, includingMarcos, Lilly, and Heather. What is the probability thatMarcos will win the 1 st prize, Lilly will win the 2 nd prize,and Heather will win the 3 rd prize?There areThere areThere arechoices for 1 st prize.choices for 2 nd prize.choices for 3 rd prize.7 · 6 · 5 = 210 The number of permutations of 3 prizes.There arepossible arrangements, or permutations, ofthe 3 prizes. Since there is only one way of arranging Marcosfirst, Lilly second, and Heather third, the probability of thisevent is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress CLUBS The president andvice president of the French Club will be randomly selectedfrom a jar of 24 names. Find the probability that Sophie will beselected as president and Peter selected as vice president.Math Connects, Course 2 211

9–5 CombinationsMAIN IDEA• Find the number ofcombinations of a setof objects and findprobabilities.BUILD YOUR VOCABULARY (pages 202–203)An arrangement, or listing, of objects in which order isis called a combination.EXAMPLE Find the Number of CombinationsDECORATING Ada can select from seven paint colorsfor her room. She wants to choose two colors to paintstripes on her walls. How many different pairs of colorscan she choose?METHOD 1 Make a list.Number the colors 1 through 7.1, 2 1, 5 2, 3 2, 6 3, 5 4, 5 5, 61, 3 1, 6 2, 4 2, 7 3, 6 4, 6 5, 71, 4 1, 7 2, 5 3, 4 3, 7 4, 7 6, 7®ORGANIZE ITOn the tab for Lesson9–5, record whatyou learn aboutcombinations. Be sureto compare and contrastcombinations andpermutations.There aredifferent pairs of colors.METHOD 2 Use a permutation.There are 7 · 6 permutations of two colors chosen from seven.There are 2 · 1 ways to arrange the two colors._ 7 · 62 · 1 = =There aredifferent pairs of colors Ada can choose.Check Your Progress HOCKEY The Brownsville Badgershockey team has 14 members. Two members of the team areto be selected to be the team’s co-captains. How many differentpairs of players can be selected to be the co-captains?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.212 Math Connects, Course 2

9–5REMEMBER ITTo find a combinationyou must divide thepermutation by thenumber of ways youcan arrange the items.EXAMPLESINTRODUCTIONS Ten managers attend a businessmeeting. Each person exchanges names with each otherperson once. How many introductions will there be?There are 10 · 9 ways to choose 2 people.There are 2 · 1 ways to arrange the 2 people._ 10 · 92 · 1 = _ 902 orThere areintroductions.If the introductions in Example 2 are made at random,what is the probability that Ms. Apple and Mr. Zimmerwill be the last managers to exchange names?Since there areintroductions and only one favorableoutcome, the probability that Ms. Apple and Mr. Zimmer will bethe last managers to exchange names is .Check Your ProgressCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:a. INTRODUCTIONS Fifteen managers attend a businessmeeting. Each person exchanges names with each otherperson once. How many introductions will there be?b. What is the probability that Ms. Apple and Mr. Zimmer willbe the last managers to exchange names?Math Connects, Course 2 213

9–6 Problem-Solving Investigation: Act It OutEXAMPLE Solve Using the Act It Out StrategyMAIN IDEA• Solve problems byacting it out.LUNCH Salvador is looking for his lunch money,which he put in one of the pockets of his backpackthis morning. If the backpack has six pockets, what isthe probability that he will find the money in the firstpocket that he checks?UNDERSTAND You know that there arepockets inSalvador’s backpack and that one of thepockets contains his lunch money.PLANSOLVEToss a number cube several times. If the cubelands on 1, Salvador will find the money in thefirst pocket that he checks. If the cube lands on2, 3, 4, 5, or 6, Salvador will not find the moneyin the first pocket that he checks.Toss the cube and make a table of the results.Trials 1 2 3 4 5 6 7 8 9 10 11 12HOMEWORKASSIGNMENTPage(s):Exercises:Outcome 4 5 1 2 2 3 6 4 5 2 1 3CHECKThe highlighted entries show thatout ofthe 12 trials resulted in Salvador finding hislunch money in the first pocket that he checks.So, the probability is 2_12 or .Repeat the experiment several times to seewhether the results agree.Check Your Progress PHOTOGRAPHS A photographeris taking a picture of the four members in Margaret’s family.Margaret’s grandmother will stand on the right. How manydifferent ways can the photographer arrange the familymembers in a row for the photo?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.214 Math Connects, Course 2

9–7 Theoretical and Experimental ProbabilityMAIN IDEA• Find and compareexperimentaland theoreticalprobabilities.®ORGANIZE ITOn the tab forLesson 9-7, take notesabout theoretical andexperimental probability.Be sure to describe theirdifferences.BUILD YOUR VOCABULARY (pages 202–203)Experimental probability is based on whatoccurred during an experiment. Theoretical probability isbased on whatexperiment.EXAMPLE Experimental Probabilityhappen when conducting anA spinner is spun 50 times, and it lands on the colorblue 15 times. What is the experimental probability ofspinning blue?P(blue) =number of timesis spun______number ofoutcomesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= __ orThe experimental probability of spinning the color blue is .Check Your Progress A marble is pulled from a bag ofcolored marbles 30 times and 18 of the pulls result in a yellowmarble. What is the experimental probability of pulling ayellow marble?Math Connects, Course 2 215

9–7EXAMPLES Experimental and Theoretical ProbabilityThe graph shows the results of an experiment in which anumber cube is rolled 30 times.Find the experimental probability of rolling a 5.number of times occursP(5) = ______number of possible outcomes= __ orNumber of Rolls9876543The experimental probability of rollinga is .2101 2 3 4 5 6NumberCompare the experimental probability of rolling a 5 toits theoretical probability.The theoretical probability of rolling a 5 on a number cubeis. So, the theoretical probability is close to theexperimental probability of .HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress The graph shows the result of anexperiment in which a coin was tossed 150 times.a. Find the experimentalCoin Tossprobability of tossing100heads for this90experiment.80b. Compare theexperimentalprobability of tossingheads to its theoreticalprobability.Number of Tosses706050403020100HeadsTailsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.216 Math Connects, Course 2

9–8Compound EventsMAIN IDEA• Find the probabilityof independent anddependent events.KEY CONCEPTBUILD YOUR VOCABULARY (pages 202–203)A compound event consists of two or moreevents.When choosing one event does notchoosing asecond event, both events are called independent events.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Probability of TwoIndependent Events Theprobability of twoindependent events canbe found by multiplyingthe probability ofthe first event by theprobability of the secondevent.®On the tabfor Lesson 9-8, givean example of findingthe probability of twoindependent events.EXAMPLE Independent EventsLUNCH For lunch, Jessica may choose from a turkeysandwich, a tuna sandwich, a salad, or a soup. Fora drink, she can choose juice, milk, or water. If shechooses a lunch and a drink at random, what is theprobability that she chooses a sandwich (of either kind)and juice?P(sandwich) = P(juice) =P(sandwich and juice) = · orSo, the probability that she chooses a sandwich and juice is .Check Your Progress SWEATS Zachary has a blue, a red,a gray, and a white sweatshirt. He also has blue, red, and graysweatpants. If Zachary randomly pulls a sweatshirt and a pairof sweatpants from his drawer, what is the probability thatthey will both be blue?BUILD YOUR VOCABULARY (pages 202–203)If one event affects the outcome of a second event, theevents are called dependent events.If two events cannot happen at the same time, then theyare disjoint events.Math Connects, Course 2 217

9–8EXAMPLES Dependent EventsSOCKS There are 4 black, 6 white, and 2 blue socksin a drawer. José randomly selects two socks withoutreplacing the first sock. What is the probability that heselects two white socks?P(first sock is white) = 6 _12There are white socksand total socks.KEY CONCEPTProbability of twoDependent Events Theprobability of twodependent events,A and B, can be foundby multiplying theprobability of A by theprobability of B afterA occurs.HOMEWORKASSIGNMENTPage(s):Exercises:®On the tabfor Lesson 9-8, givean example of findingthe probability of twoindependent events.P(second sock is white) = 5 _11P(two white socks) =Disjoint Events6_After one white sock is removed,there are12 · _ 511 ortotal socks.white socks andMONTHS A month of the year is randomly selected.What is the probability of the month ending in theletter Y or the letter R.They are disjoint events since it is impossible to have a monthending in both the letter Y and the letter R?P(ending in Y or R) = _Check Your Progress12There are 8 months that endin Y or R.There are 12 months.a. GAMES Janet has a card game that uses a deck of48 cards – 16 red, 16 blue, and 16 green. If she randomlyselects two cards without replacing the first, what is theprobability that both are green?b. MARBLES There are 12 yellow, 3 black, 5 red, and 8 bluemarbles in a bag. Joseph randomly selects one marble fromthe bag. What is the probability that the marble selected willbe black or red?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.218 Math Connects, Course 2

C H A P T E R9BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 9 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 9, go to:glencoe.comYou can use your completedVocabulary Builder(pages 202–203) to help yousolve the puzzle.9-1Simple EventsFor Questions 1–3, a bag contains 4 green, 6 orange, and10 purple blocks. Find each probability if you draw one blockat random from the bag. Write as a fraction in simplest form.1. P(green) 2. P(orange) 3. P(purple)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9-2Sample Spaces4. PHONES A phone company offers three different calling features(caller ID, call waiting, and call forward) and two different callingplans (Plan A or Plan B). Find the sample space for all possibilitiesof a calling feature and a calling plan.Math Connects, Course 2 219

Chapter 9 BRINGING IT ALL TOGETHER9-3The Fundamental Counting Principle5. Underline the correct term to complete the sentence: Theoperation used in the Fundamental Counting Principle is(addition, multiplication).Use the Fundamental Counting Principle to find the totalnumber of outcomes in each situation.6. Tossing a coin and rolling a 6-sided number cube.7. Making a sandwich using whole wheat or sourdough bread, hamor turkey, and either cheddar, swiss, or provolone cheese.8. Choosing a marble from a bag containing 10 differently coloredmarbles and spinning the spinner at the right.9-4Permutations9. LETTERS How many permutations are there of the letters inthe word pizza?10. BASEBALL In how many ways can the six infielders of a baseballteam stand in a row for autograph signing?11. NUMBERS How many 4-digit passwords can be formed usingthe digits 1, 3, 4, 5, 7, and 9? Assume no number can be usedmore than once.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.220 Math Connects, Course 2

Chapter 9 BRINGING IT ALL TOGETHER9-5CombinationsComplete each sentence.12. You can find the number or combinations of objects in a set bythe number ofof the entireset by the number of ways each smaller set can be arranged.13. A is an arrangement or listing in which orderis not .14. The burger shop offers 3 choices of condiments from the following:lettuce, onions, pickles, ketchup, and mustard. How manydifferent combinations of condiments can you have on yourburger?9-6Problem-Solving Investigation: Act It OutCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.15. TRAVEL Four friends are driving to the beach. In how manydifferent ways can two friends sit in the front and two friends sitin the back if Raul must be the driver?9-7Theoretical and Experimental ProbabilityUnderline the correct term(s) to complete each sentence.16. The word experimental means based on (experience, theory).17. Theoretical probability is based on what (you actually try,is expected).18. (Experimental, theoretical) probability can be based on pastperformance and can be used to make predictions about futureevents.Math Connects, Course 2 221

Chapter 9 BRINGING IT ALL TOGETHERSue has 5 different kinds of shoes: sneakers, sandals, boots,moccasins, and heels.19. If she chooses a pair each day for two weeks, and choosesmoccasins 8 times, what is the experimental probability thatmoccasins are chosen?20. Find the theoretical probability of choosing the moccasins.9-8Compound EventsState whether each sentence is true or false. If false, replacethe underlined word to make the sentence true.21. A compound event consists of more than one single event.22. When the outcome of the first event does not have any effect onthe second event it is called a simple event.23. A yellow and a green cube are rolled. What is the probability thatan even number is rolled on the yellow cube and a number lessthan 3 is rolled on the green cube?24. There are 4 chocolate chip, 6 peanut butter, and 2 sugar cookies ina box. Malena randomly selects two cookies without replacing thefirst. Find the probability that she selects a peanut butter cookieand then a sugar cookie.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.222 Math Connects, Course 2

C H A P T E R9ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 9.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 9 Practice Test onpage 503 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 9 Study Guide and Reviewon pages 498–502 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 9 Practice Test onpage 503 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 9 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 9 Study Guide and Review onpages 498–502 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 9 Practice Test onpage 503 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 223

C H A P T E R10Geometry: Polygons®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" by 17 " paper.Fold a 2" tab along thelong side of the paper.Unfold the paper andfold in thirds widthwise.Open and draw linesalong the folds. Labelthe head of each columnas shown. Label the frontof the folded table withthe chapter title.NOTE-TAKING TIP: As you study a chapter, takenotes, record concepts, and write examples aboutimportant definitions and concepts.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.224 Math Connects, Course 2

C H A P T E R10BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 10.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleacute triangleadjacent anglescomplementary anglescongruent anglesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.congruent segmentsequilateral [EH-kwuh-LA-tuh-rull] triangleindirect measurementisosceles [y-SAHS-LEEZ] triangleline symmetryobtuse triangleChapter 10parallelogram(continued on the next page)Math Connects, Course 2 225

Chapter 10 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplequadrilateral [KWAHdruh-LA-tuh-ruhl]reflectionrhombus [RAHM-buhs]scalene [SKAY-LEEN]trianglesimilar figuresstraight anglesupplementary anglestessellationtranslationtrapezoid [TRA-puh-ZOYD]vertexCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.vertical angles226 Math Connects, Course 2

10–1Angle RelationshipsBUILD YOUR VOCABULARY (pages 225–226)MAIN IDEA• Classify angles andidentify vertical andadjacent angles.An angle has two sides that share aendpoint and is measured in units called degrees.Thewhere the sides of an angleis called the vertex.EXAMPLE Naming AnglesName the angle at the right.• Use the vertex as the middleletter and a point from each side.or• Use the vertex only.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Use a number.The angle can be named in four ways:, , , or .Check Your Progress Name the angle below. Math Connects, Course 2 227

10–1REMEMBER ITA ray starts at apoint and goes withoutend in one direction.BUILD YOUR VOCABULARY (pages 225–226)A right angle measures 90°.An acute angle measures than 90°.An obtuse angle measures 90° and 180°.A straight angle measures 180°.EXAMPLES Classify AnglesClassify each angle as acute, obtuse, right, or straight.The angle is exactly , so it is a angle.The angle is than 90°, so it is an angle.Check Your Progress Classify each angle as acute,obtuse, right, or straight.a.b.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.228 Math Connects, Course 2

10–1BUILD YOUR VOCABULARY (pages 225–226)Two angles that have the sameTwo angles are vertical if they areare congruent.anglesformed by the intersection of two lines.Two angles are adjacent if they share a common vertex, acommon, and do not overlap.EXAMPLEDetermine if each pair of angles inthe figure at the right are verticalangles, adjacent angles, or neither.a. ∠3 and ∠5Since ∠3 and ∠5 are opposite angles formed by theintersection of two lines, they are angles.b. ∠3 and ∠4∠3 and ∠4 share a common vertex and side, and do notCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.overlap. So, they are angles.c. ∠4 and ∠5∠4 and ∠5 share a common vertex and side, and do notoverlap. So, they are angles.Check Your Progress Determine ifeach pair of angles in the figure at theright are vertical angles, adjacentangles, or neither.a. ∠1 and ∠2b. ∠2 and ∠5 c. ∠1 and ∠4Math Connects, Course 2 229

10–2Complementary and Supplementary AnglesMAIN IDEA• Identify complementaryand supplementaryangles and find missingangle measures.BUILD YOUR VOCABULARY (pages 225–226)Complementary angles have a sum of .Supplementary angles have a sum of .EXAMPLES Classify AnglesClassify each pair of angles as complementary,supplementary, or neither.128˚52˚+ 52° =So, the angles are .∠x and ∠y form axyangle.So, the angles are .Check Your Progress Classify each pair of angles ascomplementary, supplementary, or neither.a.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.230 Math Connects, Course 2

10–2REMEMBER ITWhen two anglesare congruent, themeasure of the anglesare equal.b.EXAMPLE Find a Missing Angle MeasureAngles PQS and RQS are supplementary.If m∠PQS = 56°, find m∠RQS.Since ∠PQS and ∠RQS are supplementary,m∠PQS + m∠RQS = 180°.m∠PQS + m∠RQS = 180 Write the equation.+ m∠RQS = Replace m∠PQS with .___________- 56 - 56 Subtract from each side.m∠RQS = 180 - =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:The measure of is 124°.Check Your Progress Angles MNP and KNP arecomplementary. If m∠MNP = 23°, find m∠KNP.Math Connects, Course 2 231

10–3 Statistics: Display Data in a Circle GraphMAIN IDEA• Construct and interpretcircle graphs.BUILD YOUR VOCABULARY (pages 225–226)A graph that shows data as parts of agraph.is a circleEXAMPLE Display Data in a Circle GraphSPORTS In a survey, a groupof middle school studentswere asked to name theirfavorite sport. The results areshown in the table. Make acircle graph of the data.Sport Percentfootball 30%basketball 25%baseball 22%tennis 8%other 15%• Find the degrees for each part. Round to the nearest wholedegree.WRITE ITWrite a proportion toconvert 65% to thenumber of degrees in apart of a circle graph.football:of 360° = 0.30 · 360° orbasketball: 25% of 360° = · 360° orbaseball:of 360° = 0.22 · 360° or abouttennis: 8% of 360° = · 360° or aboutother:of 360° = 0.15 · 360° or about• Draw a circle with a radius marked as shown. Then use ato draw the first angle, in this case .Repeat this step for each section.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.232 Math Connects, Course 2

10–3• Label each section of thegraph with the category andREVIEW ITExplain how to converta fraction to a decimal.(Lesson 4-5)a .. Give the graphEXAMPLE Construct a Circle GraphMOVIES Gina has the following types of movies in herDVD collection. Make a circle graph of the data.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Type of Movie Numbersaction 24comedy 15science fiction 7• Find the total number of DVDs: 24 + 15 + 7 or .• Find the that compares each number withthe . Write the ratio as a numberrounded to the nearest hundredth.action: ≈ 0.52comedy: ≈ 0.33science fiction: ≈ 0.15(continued on the next page)Math Connects, Course 2 233

10–3• Find the number of degrees foreach section of the graph. action: 0.52 · 360° =comedy: 0.33 · 360° =science 0.15 · 360° =fiction:• Draw the circle graph.Check Your Progressa. ICE CREAM In a survey, a group of students were askedto name their favorite flavor of ice cream. The results areshown in the table. Make a circle graph of the data.FlavorPercentchocolate 30%cookie dough 25%peanut butter 15%strawberry 10%other 20%b. MARBLES Michael has the following colors of marbles inhis marble collection. Make a circle graph of the data.ColorNumberblack 12green 9red 5gold 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.234 Math Connects, Course 2

10–3EXAMPLES Analyze a Circle GraphVOTING The circle graph below shows the percent ofvoters in a town who are registered with a politicalparty.Which party has the most registered voters?The largest section of the circle is the one representing. So, the Democratic party has the mostregistered voters.If the town has 3,400 registered Republicans, about howmany voters are registered in all?Republicans: 42% of registered voters =0.42 × n = 3,4000.42n = 3,400n ≈ 8,095So, there are aboutregistered voters in all.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress SPORTS The circle graph belowshows the responses of middle school students to thequestion “Should teens be allowed to play professionalsports?”a. Which response was the greatest? Should Teens Be Allowedto Play Professional Sports?b. If there were 1,500 middle schoolstudents, how many had no opinion?Yes55%No32%NoOpinion13%Math Connects, Course 2 235

10–4TrianglesMAIN IDEA• Identify and classifytriangles.BUILD YOUR VOCABULARY (pages 225–226)A triangle is a figure with threeand three.Sides with the sameare congruent segments.KEY CONCEPTAngles of a Triangle Thesum of the measures ofthe angles of a triangleis 180°.®Record thisrelationship in yourFoldable. Be sure toinclude an example.EXAMPLE Find a Missing MeasureALGEBRA Find m∠A in △ABC if m∠A = m∠B,and m∠C = 80°.Since the sum of the angle measures in a triangle is 180°,m∠A + m∠B + m∠C = .Let x represent m∠A. Since m∠A = m∠B, x also represents.x + x + 80 = 180Write the equation.+ 80 = 180 x + x = 2x- - Subtract from each side.̲̲̲̲̲̲̲̲̲̲_ 2x= _ 100 Divide each side by 2.x = So, m∠A = .Check Your Progress ALGEBRA Find m∠M in △MNOif m∠N = 75° and m∠O = 67°.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.236 Math Connects, Course 2

10–4BUILD YOUR VOCABULARY (pages 225–226)An acute triangle has all acute angles. A right triangle hasone right angle. An obtuse triangle has one obtuse angle.A scalene triangle has no congruent sides. An isoscelestriangle has at least 2 congruent sides. An equilateraltriangle has three congruent sides.EXAMPLETEST EXAMPLE An airplane haswings that are shaped like triangles. Whatis the missing measure of the angle?A 41° B 31° C 26° D 21°Read the ItemTo find the missing measure, write andsolve an equation.x˚47˚112˚Solve the Itemx + + = 180 The sum of the measures is 180.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:x + = 180 Simplify.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲-159 -159 Subtract 159 from each side.x =The missing measure is 21°. The answer is D.Check Your ProgressMULTIPLE CHOICE A piece of fabricis shaped like a triangle. Find the missingangle measure.F 73° G 49°H 58° J 53°Math Connects, Course 2 237

10–5 Problem-Solving Investigation:Use Logical ReasoningEXAMPLE Solve Using Logical ReasoningMAIN IDEA• Solve problems byusing logical reasoning.GEOMETRY Draw an equilateral triangle. How can youconfirm that it is equilateral?UNDERSTAND You know that equilateral triangles havecongruent sides. You need to confirmwhether or not a drawn triangle is equilateral.PLANDraw an equilateral triangle. Measure thesides to confirm that all three sides are.SOLVEDraw the triangle.2.6 cm 2.6 cmHOMEWORKASSIGNMENTPage(s):Exercises:CHECK2.6 cmMeasure the sides using a ruler or centimeterruler. The side lengths are 2.6 centimeters,2.6 centimeters, and 2.6 centimeters. Sinceall three sides are congruent, the triangle isequilateral.Since all three sides are congruent, thetriangle is equilateral. You can have someoneelse also measure the sides to check that thetriangle is .Check Your Progress GEOMETRY Do the angles in anequilateral triangle have a special relationship?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.238 Math Connects, Course 2

10–6 QuadrilateralsMAIN IDEA• Identify and classifyquadrilaterals.BUILD YOUR VOCABULARY (pages 225–226)A quadrilateral is afigure withsides and four .A parallelogram is a quadrilateral with opposite sidesand opposite sides .A trapezoid is awith one pair of®sides.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITRecord what you learnabout quadrilaterals.Illustrate and describethe five types ofquadrilaterals discussedin this chapter.A rhombus is a parallelogram with four congruent sides.EXAMPLES Classify QuadrilateralsClassify the quadrilateral using the name that bestdescribes it.The quadrilateral has 4angles and oppositesides are . It is a .The quadrilateral has pair of sides.It is a .Math Connects, Course 2 239

10–6KEY CONCEPTAngles of a QuadrilateralThe sum of the measuresof the angles of aquadrilateral is 360°.Check Your Progress Classify the quadrilateral usingthe name that best describes it.a.b.EXAMPLE Find a Missing MeasureALGEBRA Find the value of x in thequadrilateral shown.Write and solve an equation. Let xrepresent the missing measure.120˚60˚x˚60˚HOMEWORKASSIGNMENTPage(s):Exercises:+ + + x = 360 The sum of themeasures is 360°.+ x = 360 Simplify.̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲̲x =So, the missing angle measure is .Check Your Progressthe quadrilateral.Subtract fromboth sides.Find the missing angle measure inCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 240 Math Connects, Course 2

10–7Similar FiguresMAIN IDEA• Determine whetherfigures are similar andfind a missing length ina pair of similar figures.BUILD YOUR VOCABULARY (pages 225–226)Figures that have the samebut not necessarilythe sameare similar figures.Theof similar figures that “match” arecorresponding sides.KEY CONCEPTSimilar Figures If twofigures are similar, thenThecorresponding angles.of similar figures that “match” are• the corresponding sidesare proportional, and• the correspondingangles are congruent.EXAMPLE Identify Similar FiguresWhich rectangle below is Fsimilar to rectangle FGHI?I9 ftG3 ftHCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.LO8 ftM A 6 ft2 ftNDB Q 12 ft2 ftCCompare the ratios of the corresponding sides.Rectangle LMNO Rectangle ABCD Rectangle QRSTFG_LM = _ 9 8GH_MN =FG_AB =GH_BC = _ 3 2TFG_QR = _ 912GH_RS =So, rectangle FGHI is similar to rectangle .R6 ftSMath Connects, Course 2 241

10–7Check Your Progress Which rectangleW 4 ft Xfrom Example 1 is similar to rectangle WXYZ2 ftshown?Y ZBUILD YOUR VOCABULARY (pages 225–226)Indirect measurement uses similar figures to find the length,width, or height of objects that are too difficult to measure®directly.ORGANIZE ITUse your Foldable torecord what you learnabout similar figures andindirect measurement.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEARCHITECTURE A rectangular picture window 12 feetlong and 6 feet wide needs to be shortened to 9 feet inlength to fit a redesigned wall. If the architect wants thenew window to be similar to the old window, how widewill the new window be?_ 129 = _w6 Write a proportion.12w =12w =Find the cross products.Simplify.w = Divide each side by .So, the width of the new window will befeet.Check Your Progress Tom has a rectangular garden thathas a length of 12 feet and a width of 8 feet. He wishes to starta second garden that is similar to the first and will have awidth of 6 feet. Find the length of the new garden.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.242 Math Connects, Course 2

10–8Polygons and TessellationsMAIN IDEA• Classify polygons anddetermine whichpolygons can forma tessellation.BUILD YOUR VOCABULARY (pages 225–226)A polygon is a simple, closed figure formed by three ormore straight line segments.A regular polygon has all sides congruent and all anglescongruent.A polygon is named by the number of sides it has:pentagon (5 sides), hexagon (6 sides), heptagon (7 sides),octagon (8 sides), nonagon (9 sides), and decagon (10 sides).EXAMPLES Classify PolygonsDetermine whether each figure is a polygon.The figure is not a polygon sinceCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.it has aside.This figure has 6 sides that are notall of equal length. It is athat is not .Check Your Progress Determine whether each figureis a polygon. If it is, classify the polygon and statewhether it is regular. If it is not a polygon, explain why.a.b.Math Connects, Course 2 243

10–8ORGANIZE ITUse your Foldable torecord what you learnabout polygons andtessellations. Explainhow a tessellation can bemade with several kindsof polygons.®BUILD YOUR VOCABULARY (pages 225–226)A repetitive pattern of polygons that fit together with noorEXAMPLE Tessellationsis called a tessellation.PATTERNS Ms. Pena is creating a pattern on her wall.She wants to use regular hexagons. Can Ms. Pena makea tessellation with regular hexagons?The measure of each angle in a regular hexagon is .The sum of the measures of the angles where the verticesmeet must be 360°.So, solve 120n = 360._ 120n120 = _ 360120Write the equation.Divide each side by .n =Since 120° divides evenly into 360°, the sum of the measuresHOMEWORKASSIGNMENTPage(s):Exercises:where the vertices meet is . So, Ms. Pena canmake a tessellation with regular hexagons.Check Your Progress QUILTING Emily is making a quiltusing fabric pieces shaped as equilateral triangles. Can Emilytessellate the quilt with these fabric pieces?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.244 Math Connects, Course 2

10–9 TranslationsMAIN IDEA• Graph translationsof polygons on acoordinate plane.BUILD YOUR VOCABULARY (pages 225–226)A transformation maps one figure onto another.A translation is a transformation where a figure is movedwithout turning it.The original figure and the translated figure are congruentfigures.EXAMPLE Graph a TranslationTranslate △ABC 5 units left and 1 unit up.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITThe order of atranslation of a figuredoes not matter. Movinga figure to the side xunits and then up y unitsis the same as moving itup y units and then tothe side x units.• Move each vertex of the figure 5units left and 1 unit up. Label thenew vertices A′, B′, and C′.• Connect the vertices to draw thetriangle. The coordinates of thevertices of the new figure areand .Check Your Progress, ,Translate △DEF 3 units leftand 2 units down.AEOByyOCADBxCFxMath Connects, Course 2 245

10–9EXAMPLE Find Coordinates of a TranslationTrapezoid GHIJ has vertices G (-4, 1) , H (-4, 3,) , I (-2, 3) ,and J (-1, 1) . Find the vertices of trapezoid G′H′I′J′ aftera translation of 5 units right and 3 units down. Thengraph the figure and its translated image.Add to each x-coordinate. Add to each y-coordinate.Vertices ofTrapezoid GHIJ(x + 5, y - 3)Vertices ofTrapezoid G′H′I′J′G (-4, 1) G′ (1, -2)H (-4, 3) (-4 + 5, 3 - 3)(-2 + 5, 3 - 3)J (-1, 1) J′ (4, -2)HOMEWORKASSIGNMENTPage(s):Exercises:The coordinates of trapezoid G′H′I′J′are G′ , H′ ,I′ , and J′ .HGIyJ H IOCheck Your Progress Triangle MNO has verticesM(-5, -3), N(-7, 0), and O(-2, 3). Find the vertices oftriangle M′N′O′ after a translation of 6 units right and3 units up. Then graph the figure and its translated image.OyGxxJCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.246 Math Connects, Course 2

10–10 ReflectionsMAIN IDEA• Identify figures withline symmetry andgraph reflections ona coordinate plane.BUILD YOUR VOCABULARY (pages 225–226)Figures thatexactly when they are folded inhave line symmetry.Each fold line is called a line of symmetry.EXAMPLES Identify Lines of SymmetryLETTERS Determine whether each letter has a line ofsymmetry. If so, copy the figure and draw all lines ofsymmetry.This figure has line .There arelines of symmetry.This figure has line symmetry.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.There isThis figureline symmetry.line of symmetry.haveCheck Your Progress Determine whether each figurehas line symmetry. If so, copy the figure and draw alllines of symmetry.a. b.Math Connects, Course 2 247

10–10BUILD YOUR VOCABULARY (pages 225–226)REMEMBER ITVertices of a figurereceive double primesymbols (" ) after theyhave been transformedtwice.A reflection is a mirrorof the original figure thatis the result of a transformation over acalled aline of reflection.EXAMPLE Reflect a Figure Over the x-axisQuadrilateral QRST has vertices Q (-1, 1) , R (0, 3) , S (3, 2) ,and T (4, 0) . Graph the figure and its reflected image overthe x-axis. Then find the coordinates of the reflectedimage.The x-axis is the line of reflection. So, plot each vertex ofQ′R′S′T′ the same distance from the x-axis as its correspondingvertex on QRST.yRQQRSTTSQ′ R′S′ T′Check Your Progress Quadrilateral ABCD has verticesA (-3, 2,) B (-1, 5) , C (3, 3) , and D (2, 1) . Graph the figure andits reflection over the x-axis. Then find the coordinates of thereflected image.OyxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.248 Math Connects, Course 2

10–10EXAMPLE Reflect a Figure over the y-axisTriangle XYZ has vertices X (1, 2) , Y (2, 1) , and Z (1, -2).Graph the figure and its reflected image over the y-axis.Then find the coordinates of the reflected image.The y-axis is the line of reflection. So, plot each vertex of X′Y′Z′the same distance from the y-axis and its corresponding vertexon XYZ.XYyXYxZZCheck Your Progress Triangle QRS has vertices Q (3, 4) ,R (1, 0) , and S (6, 2) . Graph the figure and its reflection over they-axis. Then find the coordinates of the reflected image.yCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:OxMath Connects, Course 2 249

C H A P T E R10 BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 10 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 10, go to:glencoe.comYou can use your completedVocabulary Builder(pages 225–226) to help yousolve the puzzle.10-1Angle RelationshipsClassify each angle as acute, obtuse, or right.1. 2. 3.10-2Complementary and Supplementary AnglesComplete each sentence.4. The sum of the measures of angles is 180°.5. The sum of the measures of angles is 90°.6. If ∠A and ∠B are supplementary angles and m∠B = 43°, findm∠A.10-3Statistics: Display Data in a Circle GraphFind the number of degrees for each part ofthe graph at the right.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. A 8. B 9. C250 Math Connects, Course 2

Chapter 10 BRINGING IT ALL TOGETHER10-4TrianglesComplete the table to help you remember the ways toclassify triangles.Type ofTriangleClassified byAngles or SidesDescription10. acute angles11. obtuse12. sides no congruent sides13. 1 right angle14. equilateral10-5Problem-Solving Investigation: Logical ReasoningCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.15. RACES Marcus, Elena, Pedro, Keith, and Darcy ran a 2-mile race.Darcy finished directly after Pedro, Elena finished before Marcus,and Keith finished first. If Pedro finished third, order the runnersfrom first to last.10-6QuadrilateralsFind the value of x in the quadrilateral.16.75˚150˚x˚ 17.58˚45˚x˚Math Connects, Course 2 251

Chapter 10 BRINGING IT ALL TOGETHER10-7Similar Figures18. Find the value of x if △ABC ∼ △DEF.EB8xA7CD21F10-8Polygons and TessellationsUnderline the correct term to complete each sentence.19. A polygon can have (two, three) or more straight lines.20. To find the sum of the angle measures in a regular polygon, drawall the diagonals from one vertex, count the number of (angles,triangles) formed, and multiply by 180°.10-9Translations21. Triangle ABC with vertices A (2, 4) , B (-4, 6) , and C (1, -5)is translated 2 units right and 3 units down. What are thecoordinates of B?10-10ReflectionsUnderline the correct word(s) to complete the sentence.22. The image of a reflection is (larger than, the same size as) theoriginal figure.23. Triangle DEF has vertices D (-5, 2) , E (-4, -2) , and F (-3, 0) .It is reflected over the y-axis. What are the coordinates of D?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.252 Math Connects, Course 2

C H A P T E R10ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study are given witheach item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 10.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 10 Practice Test onpage 567 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 10 Study Guide and Reviewon pages 563–566 of your textbook.• If you are unsure of any concepts or skills, refer to the specificlesson(s).• You may want to take the Chapter 10 Practice Test onpage 567 of your textbook.I asked for help from someone else to complete the reviewof all or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 10 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 10 Study Guide and Review onpages 563–566 of your textbook.• If you are unsure of any concepts or skills, refer to the specificlesson(s).• You may also want to take the Chapter 10 Practice Test onpage 567 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 253

C H A P T E R11Measurement:Two- and Three-Dimensional Figures®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 8 _ 1 " by 11" construction2paper and two sheets of notebook paper.Fold the construction paperin half lengthwise. Label thechapter title on the outside.Fold the sheets ofnotebook paper in halflengthwise. Then foldtop to bottom twice.Open the notebookpaper. Cut along thesecond folds to makefour tabs.Glue the uncutnotebook paper sideby side onto theconstruction paper.Label each tab as shown.NOTE-TAKING TIP: When you take notes, it ishelpful to write key vocabulary words, definitions,concepts, or procedures as clearly and conciselyas possible.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.254 Math Connects, Course 2

C H A P T E R11BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 11.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebasecirclecircumferenceCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.composite figureconecylinderdiameteredgeChapter 11face(continued on the next page)Math Connects, Course 2 255

Chapter 11 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleheightlateral faceprismpyramidradiusrectangular prismsolidspherethree-dimensionalfiguretriangular prismvertexCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.volume256 Math Connects, Course 2

11–1Area of ParallelogramsMAIN IDEA• Find the areas ofparallelograms.KEY CONCEPTArea of a ParallelogramThe area A of aparallelogram equals theproduct of its base b andheight h.BUILD YOUR VOCABULARY (pages 255–256)The base is anyof a parallelogram.The height is the length of the segmentto the with endpoints on sides.EXAMPLE Find the Area of a ParallelogramFind the area of the parallelogram.6.4 cm7.5 cmEstimate A = · or cm 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:A = bhArea of a parallelogramA = · Replace with 7.5 and with 6.4.A =Multiply.The area of the parallelogram is square centimeters.This is the same as the estimate.Check Your Progress Find the area of the parallelogram.4 in.13 in.Math Connects, Course 2 257

11–2 Areas of Triangles and TrapezoidsEXAMPLE Find the Area of a TriangleMAIN IDEA• Find the areasof triangles andtrapezoids.KEY CONCEPTArea of a Triangle Thearea A of a triangleequals half the productof its base b and height h.Find the area of the triangle below.Estimate 1_2 (9)(3) =3.2 cm9 cmA = 1_ bh Area of a triangle.2A = 1_2Replace b with and h with .A =Multiply.The area of the triangle is 14.4 .This is close to the estimate.Check Your Progress Find the area of the triangle below.4.5 ft6 ftEXAMPLE Find the Area of a TrapezoidFind the area of the trapezoid below.4 m3 m7.6 mThe bases are meters and meters.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The height ismeters.258 Math Connects, Course 2

11–2KEY CONCEPTA = 1_ 2 h( b 1 + b 2 )Area of a trapezoidArea of a Trapezoid Thearea A of a trapezoidequals half the productof the height h and thesum of the bases b 1and b 2.A = 1_ 2 (3) Replace h with , b 1 with ,A = 1_2and b 2 with .(11.6) Add and .A =Multiply.The area of the trapezoid issquare meters.Check Your ProgressFind the area of the trapezoid below.8 cm®6 cmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the tab forLesson 11-2 of yourFoldable, record in wordsand symbols how to findthe area of triangles andtrapezoids.HOMEWORKASSIGNMENTPage(s):Exercises:12.5 cmMath Connects, Course 2 259

11–3 Circles and CircumferenceMAIN IDEA• Find the circumferenceof circles.BUILD YOUR VOCABULARY (pages 255–256)A circle is a set of all points in a plane that are thedistance from a givencalled thecenter.The diameter (d) is the distancethrough its center.aThe circumference (C ) is the distanceThe radius (r) is the distance from thea circle.to anypoint on a .An approximation often used for π (pi) is .KEY CONCEPTCircumference of a CircleThe circumference C ofa circle is equal to itsdiameter d times π, or 2times its radius r times π.EXAMPLE Find CircumferencePETS Find the circumference around the hamster’srunning wheel shown. Round to the nearest tenth.C = 2πrC = 2 (3)C =Multiply.The circumference is aboutinches.r 3 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.260 Math Connects, Course 2

REMEMBER ITAll circumferencesare estimates since 3.14 isan estimated value of pi.Check Your Progress SWIMMING POOLA new children’s swimming pool is being builtat the local recreation center. The pool iscircular in shape with a diameter of 18 feet.Find the circumference of the pool. Round tothe nearest tenth.11–318 ftEXAMPLE Find CircumferenceFind the circumference of a circle with a diameter of49 centimeters.Since 49 is a multiple of 7, use for π.C = πdCircumference of a circleC ≈ 22_722· Replace with _ and d with .7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:C ≈ 22_71C ≈· 497_1Divide by the , 7.Multiply.The circumference is about 154 .Check Your Progresswith a radius of 35 feet.Find the circumference of a circleMath Connects, Course 2 261

11–4 Area of CirclesEXAMPLES Find the Areas of CirclesMAIN IDEA• Find the areas of circles.KEY CONCEPTArea of a Circle The areaA of a circle equals theproduct of pi (π) and thesquare of its radius r.Find the area of the circle at the right.A =Area of a circleA = π · Replace r with .π 2 x 2 ENTERThe area of the circle is approximatelycentimeters.square4 cmKOI Find the area of the koi pond shown.The diameter of the pond is 3.6 meters, so theradius is 1_2 (3.6) or 1.8 meters.A = π r 22A = π ( )Area of a circleReplace r with .HOMEWORKASSIGNMENTPage(s):Exercises:A ≈Use a calculator.The area is approximately 10.2 square meters.Check Your Progressa. Find the area of the circle below.10.5 ftb. COINS Find the area of a nickel with a diameter of2.1 centimeters.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.262 Math Connects, Course 2

11–4BUILD YOUR VOCABULARY (pages 255–256)A sector of a circle is a region of a circle bounded byradii.EXAMPLETEST EXAMPLE Mr. McGowan made an apple pie with adiameter of 10 inches. He cut the pie into 6 equal slices.Find the approximate area of each slice.A 3 in 2 B 13 in 2 C 16 in 2 D 52 in 2Read the ItemYou can use the diameter to find the total area of the pie andthen divide that result by 6 to find the area of each slice.Solve the ItemFind the area of the whole pie.A =πr 2Area of a circleA = π ( )A ≈ 78Find the area of one slice.2Replace r with .Multiply.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.78 ÷ = 13The area of each slice is approximately 13 square inches.The correct answer is .Check Your Progress MULTIPLE CHOICE The floor ofa merry-go-round at the amusement park has a diameter of 40feet. The floor is divided evenly into eight sections, each havinga different color. Find the area of each section of the floor.F 15.7 ft 2 H 62.8 ft 2G 20 ft 2 J 157 ft 2Math Connects, Course 2 263

11–5 Problem-Solving Investigation:Solve a Simpler ProblemEXAMPLE Use the Solve a Simpler Problem StrategyMAIN IDEA• Solve problems bysolving a simplerproblem.PAINT Ben and Shelia aregoing to paint the wall of aroom as shown in thediagram. What is the areathat will be painted?UNDERSTAND You know the dimensions of the wall includingthe door and window. You also know thedimensions of the door and window. You needto find the area of the wall not including thedoor and window.PLANSOLVEFind the area of the wall including the doorand window. Then subtract the area of thedoor and the window.area of wall including door and window:A = lwA = 12 · 9 or square feetHOMEWORKASSIGNMENTPage(s):Exercises:CHECKarea of door:A = lwA = 3 · 7 orarea of window:A = lwA = 5 · 4 orsquare feetsquare feetThe total area to be painted is 108 - 21 - 20orsquare feet.The area to be painted is 67 square feet. Addthe area of the door and the window. 67 + 21 +20 is 108 square feet. So, the answer is correct.Check Your Progress Karen is placing a rectangular arearug measuring 8 feet by 10 feet in a rectangular dining roomthat measures 14 feet by 18 feet. Find the area of the flooringthat is not covered by the area rug.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.264 Math Connects, Course 2

11–6 Area of Composite FiguresMAIN IDEA• Find the areas ofcomposite figures.BUILD YOUR VOCABULARY (pages 255–256)A composite figure is made of triangles, quadrilaterals,semicircles, and otherfigures.A semicircle isof a circle.EXAMPLE Find the Area of a Composite FigureFind the area of the figure in square centimeters.The figure can be separatedinto aand a®of each.. Find the areaCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITIn the tab for Lesson 11-6of your Foldable, recordin words and symbolshow you find the area ofcomposite figures. Makeup an example of yourown and explain howyou would find the area.Area of Rectangle Area of TriangleA = lw A = 1_2 bhA = 15 · 10 or A = 1_ (5)(4) or2The area is 150 + 10 orCheck Your Progresssquare centimeters.Find the area of the figure shown.Math Connects, Course 2 265

11–6WRITE ITExplain in general termshow to subdivide acomposite figure so youcan find its area.EXAMPLE Find the Area of a Composite FigureWINDOWS The diagram at the rightshows the dimensions of a window.Find the area of the window. Roundto the nearest tenth.The figure can be separated into a semicircleand a rectangle.Area of SemicircleA = π r 2 Area of a semicircleA = 1_ π Replace r with ÷ or .2A ≈Simplify.Area of RectangleA = lwArea of a rectangleA = Replace l with - orand w with .HOMEWORKASSIGNMENTPage(s):Exercises:A =Multiply.The area of the window is approximately + orsquare feet.Check Your Progress The diagram below shows thedimensions of a new driveway. Find the area of the driveway.Round to the nearest tenth.21 ft9 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.266 Math Connects, Course 2

11–7 Three-Dimensional FiguresMAIN IDEA• Classify threedimensionalfigures.BUILD YOUR VOCABULARY (pages 255–256)A three-dimensional figure has length, width, and depth.A face is a flat. The edges are the segmentsformed by intersecting. The edgesat the vertices. Theare calledlateral faces.EXAMPLES Classify Three-Dimensional FiguresFor each figure, identify the shape of the base(s). Thenclassify the figure.®Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITRecord notes aboutclassifying threedimensionalfiguresunder the tab forLesson 11-7 of yourFoldable.The figure has fourtriangular faces andone rectangular base.The figure is a.The base and all otherfaces are rectangles.The figure is aCheck Your Progress For each figure, identify theshape of the base(s). Then classify the figure.a. b..Math Connects, Course 2 267

11–7BUILD YOUR VOCABULARY (pages 255–256)The top and bottom faces of a three-dimensional figure arecalled the bases.A prism has at least three lateral faces that are rectangles.A pyramid has at least three lateral faces that are triangles.A cone has one base that is aand one vertex.A cylinder has two bases that arecircles.All of the points on a sphere are the same distance fromthe center.EXAMPLEREMEMBER ITThe base tells thename of the threedimensionalfigure.HOMEWORKASSIGNMENTPage(s):Exercises:HOUSES Classify the shape of the house’s roof as athree-dimensional figure.The shape of the house’s roofis a .Check Your Progress Classify the shape of the houseabove, not including the roof.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.268 Math Connects, Course 2

11–8 Drawing Three-Dimensional FiguresEXAMPLE Draw a Three-Dimensional FigureMAIN IDEADraw a top, a side, and a front view of the figure below.• Draw a threedimensionalfiguregiven the top, side, andfront views.The top and front views areview is a .. The side®ORGANIZE ITRecord notes aboutdrawing threedimensionalfiguresunder the tab forLesson 11-8 in yourFoldable. Sketchexamples of rectangularprisms and cylinders.Check Your Progressof the figure below.Draw a top, a side, and a front viewCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Math Connects, Course 2 269

11–8EXAMPLE Draw a Three-Dimensional FigureREMEMBER ITThere is more thanone way to draw thedifferent views of athree-dimensional figure.Draw the three-dimensional figure whose top, side, andfront views are shown below. Use isometric dot paper.Step 1 Use the top view to draw the base of the figure.Step 2Step 3Add edges to make the base a solid figure.Use the side and front views to complete the figure.Check Your Progress Draw a solid using the top, side, andfront views shown below. Use isometric dot paper. HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.270 Math Connects, Course 2

11–9Volume of PrismsMAIN IDEA• Find the volumesof rectangular andtriangular prisms.BUILD YOUR VOCABULARY (pages 255–256)A volume of a three-dimensional figure is the measure ofoccupied by it.A rectangular prism is a prism that has rectangular. A triangular prism has bases.EXAMPLE Volume of a Rectangular PrismFind the volume of the rectangular prism.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTVolume of a RectangularPrism The volume V of arectangular prism is thearea of the base B timesthe height h. It is also theproduct of the lengthl, the width w, and theheight h.HOMEWORKASSIGNMENTPage(s):Exercises:V = lwhVolume of aV = Replace l with , w with ,and h with .V =Multiply.The volume is 24centimeters.Check Your Progress Find the volume of therectangular prism.Math Connects, Course 2 271

11–10 Volume of CylindersEXAMPLE Find the Volume of a CylinderMAIN IDEA• Find the volumes ofcylinders.Find the volume of the cylinder. Round to the nearesttenth.V =V = πVolume of a cylinderReplace the variables.V ≈ Use 3.14 for π.The volume is aboutcubic centimeters.KEY CONCEPTVolume of a Cylinder Thevolume V of a cylinderwith radius r is the areaof the base B times theheight h.®Take notes onhow to find the volumeof cylinders under the tabfor Lesson 11-10 of yourFoldable.Check Your Progress Find the volume of the cylinder.Round to the nearest tenth.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.272 Math Connects, Course 2

11–10EXAMPLECOFFEE How much coffee can the can hold?WRITE ITExplain how you woulduse a calculator toevaluate a power.V = π r 2 h2V = π ( )V ≈Volume of a cylinderReplace r with and h with .Simplify.The coffee can holds aboutcubic inches.Check Your Progress JUICE Find the volume of acylinder-shaped juice can that has a diameter of 5 inchesand a height of 8 inches.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 2 273

C H A P T E R11BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 11 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 11, go to:glencoe.comYou can use your completedVocabulary Builder(pages 255–256) to help yousolve the puzzle.11-1Area of ParallelogramsState whether each sentence is true or false. If false, replacethe underlined word to make a true sentence.1. To find the base of a parallelogram, draw a segmentperpendicular to the base with endpoints on oppositesides of the parallelogram.2. The area of a parallelogram is found by multiplying its basetimes the height.3. What is the area of a parallelogram with a base of 15 feet anda height of 3.5 feet?11-2Area of Triangles and TrapezoidsComplete the sentence.4. To find the of a triangle, find the distance fromthe to the vertex.Find the area.5.135126.9 in.7 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.13 in.274 Math Connects, Course 2

Chapter 11 BRINGING IT ALL TOGETHER11-3Circles and CircumferenceFind the circumference of each circle. Use 3.14 or 22 for π.7Round to the nearest tenth if necessary.7. radius = 7.4 cm 8. radius = 3 1_2 in._9. diameter = 6 1_ ft 10. diameter = 1.7 mi811-4Area of CirclesComplete each sentence.11. To find the of a circle when you are given the, divide the length of the diameter by ,Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.square that, andthe result by pi.12. The units for the of a circle will always be measuredinunits.13. Find the area of a circle with a diameter of 13.6 inches. Roundto the nearest tenth.11-5Problem-Solving Investigation: Solve a Simpler Problem14. MOVIES Five friends, Marcy, Luke, Shawnda, Jorge, and Lily satin a row at the movie theater. Marcy and Luke sat next to eachother, Jorge did not sit next to Luke, and Shawnda sat at the rightend. If Lily sat next to Shawnda and Jorge, find the order of thefriends’ seating from left to right.Math Connects, Course 2 275

Chapter 11 BRINGING IT ALL TOGETHER11-6Area of Composite FiguresName the two dimensions of the following figures.15. rectangle16. triangleFind the area of each figure. Round to the nearest tenth ifnecessary.17. 4 in.18. 3 cm8 in.4 in.7 cm12 in.11-7Three-Dimensional FiguresFor each figure, identify the shape of the base(s). Then classifythe figure.19. 20.21. MONUMENTS Ginger made a scale model of theWashington Monument as shown. What geometricfigure is represented by the top figure of the monument?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.276 Math Connects, Course 2

Chapter 11 BRINGING IT ALL TOGETHER11-8Drawing Three-Dimensional FiguresComplete each sentence.22. A two-dimensional figure has two dimensions:and .23. A three-dimensional figure has three dimensions: ,and .11-9Volume of PrismsFind the volume of rectangular prisms with these dimensions.Round to the nearest tenth if necessary.24. 4 ft by 12 ft by 7 ft 25. 9 in. by 8 in. by 5.5 in.26. 2.5 in. by 6 in. by 5 in. 27. 3.8 cm by 2.4 cm by 2 cmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11-10Volume of CylindersWrite C if the phrase is true of a cylinder, P if it is true of aprism, and CP if the phrase is true of both.28. has bases that are parallel and congruent.29. has sides and bases that are polygons.30. has bases that are circular.31. is a solid.32. has volume.33. is three-dimensional.Math Connects, Course 2 277

C H A P T E R11Checklist ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 11.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 11 Practice Test onpage 631 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 11 Study Guide and Reviewon pages 626–630 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 11 Practice Test onpage 631 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 11 Foldable.• Then complete the Chapter 11 Study Guide and Review onpages 626–630 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 11 Practice Test onpage 631 of your textbook.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature278 Math Connects, Course 2

C H A P T E R12Geometry and MeasurementChapter 12®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" by 17 " paper.Fold the paperin fourthslengthwise.Fold a 2" tabalong the shortside. Then foldthe rest in half.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Draw lines alongfolds and labelas shown.NOTE-TAKING TIP: When taking notes about3-dimensional figures, it is important to drawexamples. It also helps to record any measurementformulas.Math Connects, Course 2 279

C H A P T E R12BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 12.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplehypotenuseirrational numberlegPythagorean Theoremsurface areaCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.280 Math Connects, Course 2

12–1Estimating Square RootsEXAMPLE Estimate the Square RootMAIN IDEA• Estimate square roots.Estimate √ 96 to the nearest whole number.List some perfect squares.1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…81 < 96 < 100 96 is between thesquares and .< √ 96 < Find the √ of each number.< √ 96 < = 9 and= 10Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.So, √ 96 is between and . Since 96 is closertothan 81, the best whole number estimate is. Verify with a calculator.Check Your Progress Estimate each square root to thenearest whole number.a. √ 41b. √ 86c. √ 138Math Connects, Course 2 281

12–1BUILD YOUR VOCABULARY (page 280)A number that cannot be written as aisan irrational number.EXAMPLE Use a Calculator to EstimateREMEMBER ITGraph √ 37 on a number line.Decimals used torepresent irrationalnumbers are estimates,not exact values.2nd√ 37 ≈[ √ ] 37 ENTER Check = 36 and = 49. Since is between36 and 49, the answer, , is reasonable.Check Your Progressnumber line.Graph each number on aa. √ 78HOMEWORKASSIGNMENTPage(s):Exercises:b. √ 96c. √ 1882 3 4 5 6 7 8 9 104 5 6 7 8 9 10 11 127 8 9 10 11 12 13 14 15Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.282 Math Connects, Course 2

12–2 The Pythagorean TheoremMAIN IDEA• Find length using thePythagorean Theorem.BUILD YOUR VOCABULARY (page 280)The two sidesto the rightof a right triangle are the legs.The side the right of a righttriangle is the hypotenuse.The Pythagorean Theorem describes the relationshipKEY CONCEPTPythagorean TheoremIn a right triangle, thesquare of the length ofthe hypotenuse equalsthe sum of the squares ofthe lengths of the legs.between the length of theand thelengths of the .EXAMPLE Find the Length of the HypotenuseFind the length of the hypotenuse of the triangle.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.c 2 = a 2 + b 2c mm6 mm2 mmPythagorean Theoremc 2 = Replace a with 2 and b with 6.c 2 = 4 + 36 Evaluate 2 2 and 6 2 .c 2 = 40Add.c = ± √ 40 Defi nition of square rootc = ±6.3Simplify.The length of the hypotenuse is aboutmillimeters.Math Connects, Course 2 283

12–2Check Your Progress Find the length of the hypotenuse ofa right triangle if the legs are 5 centimeters and 7 centimeters.REVIEW ITHow do you know ifa triangle is a righttriangle? (Lesson 10-4)EXAMPLESPORTS A gymnasticstumbling floor is in the shapeof a square. If a gymnast flipsfrom one corner to the oppositecorner, about how far has he flipped?To solve, find the length of the hypotenuse c.c 2 = a 2 + b 2Pythagorean Theoremc 2 = + 12 2 Replace a with and b with .c 2 = 144 + Evaluate .c 2 =Add.√ c 2 = ± Take the of each side.c ≈ ±Simplify.The gymnast will have flipped about .Check Your Progress SEWING Rose has a rectangularpiece of fabric 28 inches long and 16 wide. She wants todecorate the fabric with lace sewn across both diagonals.How much lace will Rose need?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.284 Math Connects, Course 2

12–2EXAMPLE Find the Length of a LegFind the missing measure ofthe triangle at the right.15 cma9 cmc 2 = a 2 + b 22= a 2 +2Pythagorean TheoremReplace b with andc with .= a 2 + Evaluate and .225 - = a 2 + 81 - Subtract from each side.= a 2 Simplify.√ 144 = √ a 2Take theof each side.= a Simplify.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:The length of the leg iscentimeters.Check Your Progress Find the missing measure of thetriangle. Round to the nearest tenth if necessary.7 in.20 in.b in.Math Connects, Course 2 285

12–3 Problem-Solving Investigation:Make a ModelMAIN IDEA• Solve problems bymaking a model.EXAMPLE Make a Model to Solve the ProblemSTORAGE A daycare center plans to make simplewooden storage bins for the 3-inch square alphabetblocks. If each bin will hold 30 blocks, give two possibledimensions for the inside of the bin.UNDERSTAND You know the dimensions of the blocks andthat each bin holds 30 blocks. You need to givetwo possible dimensions for the inside of thebin.PLANSOLVEMake a cardboard model of a cube with sides3 inches long. Then use your model todetermine the dimensions of the bin that willhold 30 cubes.HOMEWORKASSIGNMENTPage(s):Exercises:CHECKA bin that holds 5 cubes in length, 3 cubes inwidth, and 2 cubes in height would hold 30cubes. This bin would be 15 inches in length,9 inches in width, and 6 inches in height. A binthat holds 6 cubes in length, 5 cubes in width,and 1 cube in height would also hold 30 cubes.This bin would be 18 inches in length, 15inches in width, and 3 inches in height.A bin that is 15 in. × 9 in. × 6 in. would hold15 ÷ 3 or cubes by 9 ÷ 3 or 3 cubes by6 ÷ 3 or cubes in height.This is 5 × 3 × 2 orcubes.A bin that is 18 in. × 15 in. × 3 in. would hold18 ÷ 3 or 6 cubes by 15 ÷ 3 or 5 cubes by3 ÷ 3 or 1 cube. This is 6 × 5 × 1 or 30 cubes.Check Your Progress FRAMES A photo that is 5 inchesby 7 inches will be placed in a frame that has a metal border of1.5 inches on each side. What are the dimensions of the frame?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.286 Math Connects, Course 2

12–4 Surface Area of Rectangular PrismsMAIN IDEA• Find the surface areasof rectangular prisms.BUILD YOUR VOCABULARY (page 280)The of the areas of all of the ,or faces, of afigure is thesurface area.EXAMPLE Use a Net to Find Surface AreaKEY CONCEPTSurface Area ofRectangular PrismsThe surface area S of arectangular prism withlength l, width w, andheight h is the sum of theareas of the faces.Find the surface area of the rectangular prism.You can use a net of the rectangularprism to find its surface area. Thereare three pairs of congruent faces.• top and bottom• front and back• two sides6 cmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Faces Areatop and bottom 2 (6 · 2) =front and back 2 (6 · 3) =two sides 2 (2 · 3) =The surface area is + + or squarecentimeters.Check Your Progressrectangular prism.3 cm2 cmside2 cm3 cmtopfrontbottomback6 cmFind the surface area of the2 cmside2 cm3 cm3 cmMath Connects, Course 2 287

12–4®ORGANIZE ITInclude information inwords and symbols onhow to find the surfacearea of rectangularprisms in the appropriatesection of your Foldabletable.EXAMPLE Use a Formula to Find Surface AreaFind the surface area of the rectangular prism.Replace l with , w with , and h with .surface area = 2lw + 2lh + 2wh= + += + +Multiply fi rst.Then add.=The surface area of the prism is .Check Your Progressrectangular prism.Find the surface area of the Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.288 Math Connects, Course 2

12–4EXAMPLEBOXES Drew is putting together a cardboard box thatis 9 inches long, 6 inches wide, and 8 inches high. Hebought a roll of wrapping paper that is 1 foot wide and3 feet long. Did he buy enough to wrap the box? Explain.Step 1 Find the surface area of the box.Replace l with , w with , and h with .surface area = + +=Step 2 Find the area of the wrapping paper.1 ft 3 ftarea = 12 in. · 36 in. or 432 in 2Since 432348, Drew bought enough wrapping paper.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress FABRIC Angela needs to covera cardboard box that is 15 inches long, 5 inches wide, and4 inches high with felt. She bought a piece of felt that is1 foot wide and 2 1_ feet long. Did she buy enough felt to2cover the box? Explain.Math Connects, Course 2 289

12–5Surface Area of CylindersEXAMPLE Find Surface Area of a CylinderMAIN IDEA• Find the surface areasof cylinders.Find the surface area of the cylinder. Round to thenearest tenth.KEY CONCEPTSurface Area of aCylinder The surfacearea S of a cylinder withheight h and radius ris the sum of the areasof circular bases andthe area of the curvedsurface.S =Surface area of a cylinder= 2π + 2π r = , h =≈Simplify.The surface area is aboutsquare centimeters.EXAMPLEGIFT WRAP A poster is contained in a cardboard cylinderthat is 10 inches high. The cylinder’s base has a diameterof 8 inches. How much paper is needed to wrap thecardboard cylinder if the ends are to be left uncovered?Since only the curved side of the cylinder is to be covered, youdo not need to include the areas of the top and bottom of thecylinder.S == r = 4, h = 10≈About 251.3Curved surface of a cylinderSimplify.of paper is needed.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.290 Math Connects, Course 2

12–5®ORGANIZE ITInclude information inwords and symbols abouthow to find the surfacearea of a cylinder in theappropriate section ofyour Foldable table.Check Your Progressa. Find the surface area of the cylinder. Round to the nearesttenth.b. LABELS A can of fruit juice is in the shape of a cylinderwith a diameter of 6 inches and a height of 12 inches. Howmuch paper is needed to create the label if the ends are to beleft uncovered?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 2 291

C H A P T E R12BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 12 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 12, go to:glencoe.comYou can use your completedVocabulary Builder(page 280) to help yousolve the puzzle.12-1Estimating Square RootsEstimate each square root to the nearest whole number.1. √ 95 2. √ 513. √ 150 4. √ 23012-2The Pythagorean TheoremState whether each sentence is true or false. If false, replacethe underlined word to make a true sentence.5. The Pythagorean Theorem states that c 2 = a 2 + b 2 , where arepresents the length of the hypotenuse.6. The hypotenuse is always the longest of the three sides of a righttriangle.Find the missing measure of each right triangle. Round to thenearest tenth if necessary.7.8.3 in.8 in.24 ydCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.12 yd292 Math Connects, Course 2

Chapter 12 BRINGING IT ALL TOGETHER12-3Problem-Solving Investigation: Make a Model9. BOOKS A bookstore will arrange 4 books in a row in the storewindow. In how many different ways can the store arrangethese 4 books?12-4Surface Area of Rectangular PrismsFind the surface area of each rectangular prism. Round tothe nearest tenth if necessary.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10.11.12.Math Connects, Course 2 293

Chapter 12 BRINGING IT ALL TOGETHER12-5Surface Area of CylindersWrite the formula to find each of the following.13. the area of a circle14. the circumference of a circle15. the area of a rectangleFind the surface area of the cylinder. Round to the nearesttenth if necessary.16. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.294 Math Connects, Course 2

C H A P T E R12ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 12.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 12 Practice Test onpage 663 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 12 Study Guide and Reviewon pages 660–662 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 12 Practice Test onpage 663 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 12 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 12 Study Guide and Review onpages 660–662 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 12 Practice Test onpage 663 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 2 295