Chapter 1 - XYZ Custom Plus

More documents

Recommendations

Info

18<strong>Chapter</strong> 1 The BasicsProperty 1Multiplying the numerator and denominator of a fraction by the samenonzero number never changes the value of the fraction.Property 2Dividing the numerator and denominator of a fraction by the same nonzeronumber never changes the value of the fraction.2. Write _ 5 as an equivalent fractionwith denominator848.Example 2Write _3 as an equivalent fraction with denominator 20.4Solution The denominator of the original fraction is 4. The fraction we are tryingto find must have a denominator of 20. We know that if we multiply 4 by 5, weget 20. Property 1 indicates that we are free to multiply the denominator by 5 aslong as we do the same to the numerator._ 3 4 = 3 _ ⋅ 5 = 15_4 ⋅ 5 20 The fraction _1520 is equivalent to the fraction 3 _4 .C Absolute ValuesRepresenting numbers on the number line lets us give each number two importantproperties: a direction from zero and a distance from zero. The directionfrom zero is represented by the sign in front of the number. (A number without asign is understood to be positive.) The distance from zero is called the absolutevalue of the number, as the following definition indicates.DefinitionThe absolute value of a real number is its distance from zero on thenumber line. If x represents a real number, then the absolute value of x iswritten | x |.Write each expression withoutabsolute value bars.3. | 7 |Example 3Write the expression | 5 |without absolute value bars.Solution | 5 | = 5 The number 5 is 5 units from zero4. | −7 |5. | − 3 _4 | Answers2. 30 _48 3. 7 4. 7 5. 3 _4 Example 4Write the expression | −5 |without absolute value bars.Solution | −5 | = 5 The number −5 is 5 units from zeroExample 5Write the expression | − 1 _2 | without absolute value bars.Solution| − 1 _2 | = 1 _2 The number − 1 _2 is 1 _ unit from zero2The absolute value of a number is never negative. It is the distance the numberis from zero without regard to which direction it is from zero. When workingwith the absolute value of sums and differences, we must simplify the expression
1.2 Real Numbers19inside the absolute value symbols first and then find the absolute value of thesimplified expression.ExamplesSimplify each expression.6. | 8 − 3 | = | 5 | = 57. | 3 ⋅ 2 3 + 2 ⋅ 3 2 | = | 3 ⋅ 8 + 2 ⋅ 9 | = | 24 + 18 | = | 42 | = 428. | 9 − 2 | − | 6 − 8 | = | 7 | − | −2 | = 7 − 2 = 5Simplify each expression.6. | 7 − 2 |7. | 2 ⋅ 3 2 + 5 ⋅ 2 2 |8. | 10 − 4 | − | 9 − 11 |D OppositesAnother important concept associated with numbers on the number line is that ofopposites. Here is the definition.DefinitionNumbers the same distance from zero but in opposite directions from zeroare called opposites.Example 9Give the opposite of 5.NumberOppositeGive the opposite of each number.9. 8Solution 5 −5 5 and −5 are oppositesExample 10Give the opposite of −3.NumberOpposite10. −5Solution −3 3 −3 and 3 are oppositesExample 11SolutionGive the opposite of _1 4 .Number Opposite_1 4 − 1 _4 1 _4 and − 1 _ are opposites411. − 2 _3 Example 12Give the opposite of −2.3.NumberOpposite12. −4.2Solution −2.3 2.3 −2.3 and 2.3 are oppositesEach negative number is the opposite of some positive number, and each positivenumber is the opposite of some negative number. The opposite of a negativenumber is a positive number. In symbols, if a represents a positive number, then−(−a) = aOpposites always have the same absolute value. And, when you add any twoopposites, the result is always zero:a + (−a) = 0Answers6. 5 7. 38 8. 4 9. −8 10. 511. _ 2 12. 4.23
Page 2 and 3: Chapter PretestTranslate into symbo
Page 4 and 5: 4Chapter 1 The BasicsNoteIn the pas
Page 6 and 7: 6Chapter 1 The BasicsRule (Order of
Page 8 and 9: 8Chapter 1 The Basicsc. For the seq
Page 10 and 11: 10Chapter 1 The Basics39. 20 + 2(8
Page 12 and 13: 12Chapter 1 The BasicsD Applying th
Page 14 and 15: 14Chapter 1 The Basics125. Reading
Page 16 and 17: 16Chapter 1 The BasicsPractice Prob
Page 20 and 21: 20Chapter 1 The BasicsE Multiplicat
Page 22 and 23: 22NoteThe vertical linelabeled h in
Page 24 and 25: 24Chapter 1 The Basics41. | −4
Page 26 and 27: 26Chapter 1 The Basics95.96.2.75 cm
Page 28 and 29: 28Chapter 1 The BasicsCalories and
Page 30 and 31: 30Chapter 1 The Basics2. Add −2 +
Page 32 and 33: 32Chapter 1 The Basics11. Add −4
Page 34 and 35: 34Chapter 1 The BasicsB Work the fo
Page 36 and 37: 36Chapter 1 The BasicsApplying the
Page 38 and 39: 38Chapter 1 The Basics2. Subtract6
Page 40 and 41: 40Chapter 1 The Basics12. Find x in
Page 42 and 43: 42Chapter 1 The Basics35. −(5 −
Page 46 and 47: 46Chapter 1 The BasicsD Find x in e
Page 48 and 49: 48Chapter 1 The BasicsAssociative P
Page 50 and 51: 50Chapter 1 The Basics12. 3(7x −
Page 52 and 53: 52Chapter 1 The Basics24. (x + 2) +
Page 54 and 55: 54Chapter 1 The BasicsA Use the ass
Page 58 and 59: 58Chapter 1 The BasicsNoteSome stud
Page 60 and 61: 60Chapter 1 The Basics700Calories i
Page 62 and 63: 62Chapter 1 The Basicsis a geometri
Page 64 and 65: 64Chapter 1 The Basics33. 7(−2) 3
Page 66 and 67: 66Chapter 1 The Basics95. Find the
Page 69 and 70:
Division of Real Numbers 1.7Suppose
Page 71 and 72:
1.7 Division of Real Numbers71tiply
Page 73:
1.7 Division of Real Numbers73We ca
Page 76 and 77:
76Chapter 1 The BasicsC The followi
Page 78 and 79:
78Chapter 1 The Basics79. Simplify
Page 81 and 82:
Subsets of the Real Numbers 1.8In S
Page 83 and 84:
1.8 Subsets of the Real Numbers83BP
Page 85 and 86:
1.8 Problem Set85Problem Set 1.8AGi
Page 87 and 88:
1.8 Problem Set87The next two probl
Page 89 and 90:
Addition and Subtraction with Fract
Page 91 and 92:
1.9 Addition and Subtraction with F
Page 93 and 94:
1.9 Addition and Subtraction with F
Page 95 and 96:
1.9 Problem Set95Problem Set 1.9A F
Page 97 and 98:
1.9 Problem Set9737. _13 −
Page 99 and 100:
1.9 Problem Set9981. _1 2 x +
Page 101 and 102:
Chapter 1 SummaryThe number(s) in b
Page 103:
Chapter 1 Summary103Subsets of the
Page 106 and 107:
106Chapter 1 The BasicsSimplify. [1
Page 109 and 110:
Chapter 1 ProjectsThe Basicsgroup P
show all

Chapter 1 - XYZ Custom Plus

Create successful ePaper yourself

Delete template?

Save as template?