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.
Page 1 of 5
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
Page 2 of 5
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
Page 3 of 5
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
Page 5 of 5
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.
INTERNET
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
