Mixed Numbers and Improper Fractions
Mixed Numbers and Improper Fractions
Mixed Numbers and Improper Fractions
- No tags were found...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong><strong>Improper</strong> <strong>Fractions</strong>BEFORE Now WHY?You compared <strong>and</strong> orderedfractions.You’ll compare <strong>and</strong> orderfractions <strong>and</strong> mixed numbers.So you can compare long jumpdistances, as in Ex. 40.Word Watchmixed number, p. 185proper fraction, p. 185improper fraction, p. 185A mixed number has a wholenumber part <strong>and</strong> a fraction part.The number 2 3 4 is a mixed number.Model A represents 2 3 4 .Model A2 3 4 A fraction whose numerator is lessthan its denominator is called aproper fraction .A fraction is calledan improper fraction if itsnumerator is greater than or equal toits denominator. The mixed numberModel B 8 4 2 3 4 3 4 2 3 can be written as an improper4fraction by dividing each of the2 wholes into 4 equal sized parts,then counting the number of fourths.This is shown in Model B. 1 1 4Writing <strong>Mixed</strong> <strong>Numbers</strong> as <strong>Improper</strong> <strong>Fractions</strong>Words To write a mixed number as an improper fraction,multiply the whole number part <strong>and</strong> the denominator, addthe numerator, <strong>and</strong> write the sum over the denominator.with ReadingThe mixed number2 3 4 is read “two <strong>and</strong>three fourths.”<strong>Numbers</strong> 2 3 4 2 p 4 3 1 1 4 4EXAMPLE 1 Writing <strong>Improper</strong> <strong>Fractions</strong>Write (a) 3 5 6 <strong>and</strong> (b) 2 3 as improper fractions.8Solutiona. 3 5 6 3 p 6 5 2 3 36 6b. 2 8 2 p 8 3 1 9 8 8Lesson 4.6 <strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong> <strong>Improper</strong> <strong>Fractions</strong> 185
Writing <strong>Improper</strong> <strong>Fractions</strong> as <strong>Mixed</strong> <strong>Numbers</strong>Words To write an improper fraction as a mixed number,divide the numerator by the denominator <strong>and</strong> write anyremainder as a fraction.<strong>Numbers</strong> 7 3 7 3 2 R1, or 2 1 3 EXAMPLE 2 Writing <strong>Mixed</strong> <strong>Numbers</strong>with ReviewNeed help with dividingwhole numbers?See p. 690.Write 2 3 as a mixed number.63 R5, or 3 5 6 62318 5ANSWER 2 3 5 3 6 6 You can write a remainderremainderas a fraction: d.enominatorYour turn nowWrite the number as an improper fraction.1. 1 2 5 2. 2 3. 4 1 2 4. 3 3 4 Write the improper fraction as a mixed number.5. 1 711 6. 1 3 17 15 7. 8. 637EXAMPLE 3 Comparing <strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong> <strong>Fractions</strong>Compare 1 7 <strong>and</strong> 2 1 6 4 .13 2Write 2 1 4 as an improper fraction: 2 1 4 9 4 .Rewrite 1 7 9 <strong>and</strong> using the least common denominator of 12.6 4 1 7 17 6 6 22 3 41 2 9 4 9 3 2 74 3 12 Compare the fractions: 3 412 > 2 712 , so 1 7 1 > 2 6 4 .186 Chapter 4 Number Patterns <strong>and</strong> <strong>Fractions</strong>
EXAMPLE 4 Ordering <strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong> <strong>Fractions</strong>■FitnessHealthAnother fitness test of thePresidential Physical FitnessAward involves curl-ups.Boys age 12 must complete50 curl-ups in one minute.In how many seconds mustone curl-up be done?ExercisesMore Practice, p. 708Fitness The Presidential Physical Fitness Award involves a flexibility testcalled the V-sit reach. The distances, in inches, that four students wereable to reach are listed below. Order the distances from least to greatest.Solution3 5 8 3 1 7 1 342 The denominators are 8, 1 because 3 3 1 , 4, <strong>and</strong> 2. Write the numbersas improper fractions using the least common denominator of 8.3 5 8 2 9 3 3 81 3 1 8 2 4 8 8 1 7 17 4 4 22 3 4 1 3 82 7 2 7 4 2 8 2 4 8ANSWER From least to greatest, the distances are 3, 3 1 2 , 3 5 8 , <strong>and</strong> 1 7 .4INTERNETeWorkbook PlusCLASSZONE.COMGetting Ready to PracticeVocabulary Tell whether the number is a mixed number, a properfraction, or an improper fraction.1. 1 212 2. 1 217 3. 8 3 8 4. 2 120 5. Find the Error Describe <strong>and</strong>correct the error in writing5 2 as an improper fraction.32 (5 3) p 2 16 5 3 3 36. Write 1 2 as a mixed number.7Copy <strong>and</strong> complete the statement using , or .7. 3 2 _?_ 3 1 2 8. 8 3 _?_ 2 2 3 9. 2 2 1 _?_ 7 3 4 10. 2 9 3 _?_ 6 5 5 11. Walking to School You walk to <strong>and</strong> from school five days a week. Youlive a quarter mile away from the school. Write the total distance youwalk in a week as an improper fraction <strong>and</strong> as a mixed number.Lesson 4.6 <strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong> <strong>Improper</strong> <strong>Fractions</strong> 187
Practice <strong>and</strong> Problem Solvingwith HomeworkExample Exercises1 14–232 24–333 36–38, 404 36–38, 40Online ResourcesCLASSZONE.COM• More Examples• eTutorial PlusWrite an improper fraction <strong>and</strong> a mixed number to describe the model.12. 13.Write the mixed number as an improper fraction.14. 5 1 3 15. 4 2 7 16. 2 4 9 17. 3 311 18. 4 1 8 419. 3 1 5 20. 10 2 5 21. 11 3 8 22. 8 6 7 23. 4 516 Write the improper fraction as a mixed number.24. 2 7 45 67 24 25. 26. 27. 58811 28. 9 5 629. 9 9 149 30. 410 31. 5 82 1 32. 1 0713 33. 1 591 634. Critical Thinking Which number is greater, an improper fraction ora proper fraction? Explain your reasoning.35. Bubbles You are filling 5 bottles with bubble solution. To fill one bottle,you need 1 1 4 cups of water. You can find only a quarter-cup measure.How many quarter-cups of water do you need?Order the numbers from least to greatest.36. 2 2 2 , 2 2 3 , 2 211 , 2 2 033 37. 4 040 , 4 942 , 2 220 , 1 1 9 38. 7 1 5 , 7, 3 8 20 , 5 739. Writing How could you order 3 1 4 , 3 3 4 , 3 2 7 , <strong>and</strong> 3 1 from least to greatest8without writing them as improper fractions? Explain your reasoning.740. Long Jumps The top four long jumps at a track meet are 18 1 2 feet,18 2 3 feet, 18 3 4 feet, <strong>and</strong> 18 1 feet. Order the numbers from least to3greatest. What is the distance of the longest jump?Challenge Order the numbers from least to greatest.41. 9 4 9 , 9 1 120 , 9 2 140 , 1 9 28 2, 42. 11 2 37 , 3 4 1473, , 11 3 131 1 , 4 5 4188 Chapter 4 Number Patterns <strong>and</strong> <strong>Fractions</strong>
<strong>Mixed</strong> Review43. The table shows the number of households,in millions, with cable television for the yearsfrom 1996 through 2000. Use the informationin the table to graph the data in anappropriate data display. Explain yourchoice. (Lesson 3.6)Year Households1996 631997 641998 661999 672000 69Order the fractions from least to greatest. (Lesson 4.5)44. 1 118 , 1 724 , 712 , 3 4 45. 1 325 , 2 5 , 1 120 , 715 46. 1 528 , 714 , 3 8 , 5 7 Basic SkillsFind the sum or difference.47. 62448. 200849. 3258 359 1333 1699Test-Taking PracticeINTERNETState Test PracticeCLASSZONE.COM50. Multiple Choice Write thirteen sevenths numerically.3A. 1 7 B. 713 C. 1 3 D. 137751. Multiple Choice Which mixed number is equivalent to its pairedimproper fraction?F. 5 1 7 , 3 5 7 GG. .5 1 5 , 5 1 H. 3 2 5 , 2 2 10 I. 3 511 , 4 311 Missing NumeratorsCopy <strong>and</strong> complete the fractions using 2, 3, 4, 6, <strong>and</strong> 8.Each number should be chosen so that the fractions arein order from least to greatest, <strong>and</strong> each number can beused only once.? 2 4 ?12 ?16 ?20 ?18 Lesson 4.6 <strong>Mixed</strong> <strong>Numbers</strong> <strong>and</strong> <strong>Improper</strong> <strong>Fractions</strong> 189
Change language