Mixed Numbers and Improper Fractions

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the numerator, and write the sum over the denominator. Numbers 2. 3. 4. 2 p 4. 4. 3. 1. 4. 1. EXAMPLE 1 Writing Improper Fractions. Write (a) 3. 5. 6 and (b) 2. 3.
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Mixed Numbers and Improper Fractions BEFORE

Now

WHY?

You compared and ordered fractions.

You’ll compare and order fractions and mixed numbers.

So you can compare long jump distances, as in Ex. 40.

Word Watch mixed number, p. 185 proper fraction, p. 185 improper fraction, p. 185

A mixed number has a whole number part and a fraction part. 3 4

Model A

3  4

2

The number 2  is a mixed number. 3 4

Model A represents 2 . A fraction whose numerator is less than its denominator is called a proper fraction . A fraction is called an improper fraction if its numerator is greater than or equal to its denominator. The mixed number

3 4

2  Model B 8  4

3  4

3 4

2  can be written as an improper fraction by dividing each of the 2 wholes into 4 equal sized parts, then counting the number of fourths. This is shown in Model B.

11  4

Writing Mixed Numbers as Improper Fractions Words To write a mixed number as an improper fraction,

multiply the whole number part and the denominator, add the numerator, and write the sum over the denominator. 3 2p43 11 Numbers 2      4 4 4

with

Reading

The mixed number 3 4

2 is read “two and three fourths.”

EXAMPLE

1

Writing Improper Fractions

5 6

3 8

Write (a) 3  and (b) 2  as improper fractions. Solution 5

3p65

23

a. 3 6  6  6

Lesson 4.6

3

2p83

19

b. 2 8  8  8

Mixed Numbers and Improper Fractions

185

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Writing Improper Fractions as Mixed Numbers Words To write an improper fraction as a mixed number,

divide the numerator by the denominator and write any remainder as a fraction. 7 Numbers  3

2

EXAMPLE

with

Review

1 3

7  3  2 R1, or 2 

Writing Mixed Numbers

23 6

Write  as a mixed number.

Need help with dividing whole numbers? See p. 690.

5

3 R5, or 3 6 3  62 18  5 23 6

You can write a remainder remainder as a fraction:  . denom inator

5 6

ANSWER   3 

Your turn now

Write the number as an improper fraction.

2 1. 1 5

1 3. 4  2

2. 2

3 4. 3  4

Write the improper fraction as a mixed number. 17 5.  11

13 6.  6

EXAMPLE

3

17 7.  3

15 8.  7

Comparing Mixed Numbers and Fractions

17 1 6 4 1 1 9 1 Write 2  as an improper fraction: 2   . 4 4 4

Compare  and 2 .

17

9

2 Rewrite 6 and 4 using the least common denominator of 12. 17 17  2 34      6 62 12

9 93 27        4 43 12 34

27

17

1

3 Compare the fractions: 12 > 12, so 6 > 2 4.

186

Chapter 4

Number Patterns and Fractions

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EXAMPLE

Health

4

Ordering Mixed Numbers and Fractions

Fitness The Presidential Physical Fitness Award involves a flexibility test called the V-sit reach. The distances, in inches, that four students were able to reach are listed below. Order the distances from least to greatest. 5 8

3

3

17  4

1 2

3

Solution



3 1



The denominators are 8, 1 because 3   , 4, and 2. Write the numbers as improper fractions using the least common denominator of 8. ■

5 8

Fitness Another fitness test of the Presidential Physical Fitness Award involves curl-ups. Boys age 12 must complete 50 curl-ups in one minute. In how many seconds must one curl-up be done?

29 8

38 18

3 1

24 8

3    

3        

17 17  2 34      4 42 8

3          

1 2

7 2

74 24 1 2

28 8

5 8

17 4

ANSWER From least to greatest, the distances are 3, 3 , 3 , and .

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Exercises

eWorkbook Plus CLASSZONE.COM

More Practice, p. 708

Getting Ready to Practice Vocabulary Tell whether the number is a mixed number, a proper fraction, or an improper fraction. 12 1.  12

12 2.  17

3 3. 8  8

21 4.  20

5. Find the Error Describe and

correct the error in writing 2 5  as an improper fraction. 3

2

(5  3) p 2

16

5      3 3 3

12 6. Write  as a mixed number. 7

Copy and complete the statement using , or . 3 1 7.  _?_ 3  2 2

8 2 8.  _?_ 2  3 3

22 1 9.  _?_ 7  3 4

29 3 10.  _?_ 6  5 5

11. Walking to School You walk to and from school five days a week. You

live a quarter mile away from the school. Write the total distance you walk in a week as an improper fraction and as a mixed number. Lesson 4.6

Mixed Numbers and Improper Fractions

187

Page 4 of 5

Practice and Problem Solving with Example 1 2 3 4

Homework

Exercises 14–23 24–33 36–38, 40 36–38, 40

Online Resources CLASSZONE.COM

• More Examples • eTutorial Plus

Write an improper fraction and a mixed number to describe the model. 12.

13.

Write the mixed number as an improper fraction. 1 14. 5  3

2 15. 4  7

4 16. 2  9

3 17. 3  11

1 18. 4  8

4 19. 3  15

2 20. 10  5

3 21. 11  8

6 22. 8  7

5 23. 4  16

Write the improper fraction as a mixed number. 27 24.  5

45 25.  8

67 26.  8

24 27.  11

95 28.  6

99 29.  4

149 30.  10

58 31.  21

107 32.  13

159 33.  16

34. Critical Thinking Which number is greater, an improper fraction or

a proper fraction? Explain your reasoning. 35. Bubbles You are filling 5 bottles with bubble solution. To fill one bottle, 1 you need 1  cups of water. You can find only a quarter-cup measure. 4

How many quarter-cups of water do you need?

Order the numbers from least to greatest. 22 2 22 20 36. , 2 , , 2  2 3 11 33

40 49 22 1 37. , , , 1  40 42 20 9

1 38 20 38. 7 , 7, ,  5 5 7

1 3 2 1 39. Writing How could you order 3 , 3 , 3 , and 3  from least to greatest 4 4 7 8

without writing them as improper fractions? Explain your reasoning. 7 40. Long Jumps The top four long jumps at a track meet are 18  feet, 12 2 3 1 18  feet, 18  feet, and 18  feet. Order the numbers from least to 3 4 3

greatest. What is the distance of the longest jump?

Challenge Order the numbers from least to greatest. 4 11 21 19 28 41. 9 , 9 , 9 , ,  9 20 40 2 3

188

Chapter 4

Number Patterns and Fractions

3 45 2 34 147 42. 11 , , , 11 ,  11 4 7 3 13

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Mixed Review 43. The table shows the number of households,

in millions, with cable television for the years from 1996 through 2000. Use the information in the table to graph the data in an appropriate data display. Explain your choice. (Lesson 3.6)

Year

Households

1996

63

1997

64

1998

66

1999

67

2000

69

Order the fractions from least to greatest. (Lesson 4.5) 11 17 7 3 44. , , ,  18 24 12 4

13 2 11 7 45. , , ,  25 5 20 15

15 7 3 5 46. , , ,  28 14 8 7

Basic Skills Find the sum or difference. 47.

48.

624  359 

2008  1333 

49.

3258  1699 

Test-Taking Practice 50. Multiple Choice Write thirteen sevenths numerically.

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State Test Practice

3 17

7 13

A. 

CLASSZONE.COM

13 7

B. 

C. 

D. 137

51. Multiple Choice Which mixed number is equivalent to its paired

improper fraction? 1 35 7 7

GG. .5 15, 51

F. 5 , 

2 22 5 5

H. 3 , 

10 43 11 11

I. 3 , 

Missing Numerators Copy and complete the fractions using 2, 3, 4, 6, and 8. Each number should be chosen so that the fractions are in order from least to greatest, and each number can be used only once.

?  24

?  12

?  16

?  20

?  18

Lesson 4.6

Mixed Numbers and Improper Fractions

189