Page 1 of 5
Dividing Mixed Numbers
BEFORE
Now
WHY?
You divided fractions.
You’ll divide mixed numbers.
So you can plan schedules, such as
audition times in Exs. 43–45.
Modeling Division You can use a model to find the quotient
Word Watch
Review Words
compatible numbers, p. 13
mixed number, p. 244
improper fraction, p. 244
1
3
2
3
1
3
3 . Begin by drawing a model for 3 . Then divide the model
2
3
into groups of .
23
23
2
3
23
32
1
3
32
2
3
There are 5 groups of . So, 3 5.
1
3
2
3
You can also find the quotient 3 using paper and pencil, as in
part (a) of Example 1. First you have to rewrite the mixed number as an
1
3
10
3
improper fraction. In the model above, you can see that 3 .
EXAMPLE
1
1
Dividing a Mixed Number
2
10
2
10
3
3
2
a. 3 3 3 3 3
5
1
3
Write 3 as an improper fraction.
Multiply by the reciprocal of the divisor.
1
10 3
1 3 21
Use the rule for multiplying fractions.
Divide out common factors.
5
Multiply.
5
21
6
21
8
1
6
b. 2 8 6 8 1
7
5
8
Write 2 and 6 as improper fractions.
Multiply by the reciprocal of the divisor.
21 1
8 62
Use the rule for multiplying fractions.
Divide out common factors.
7
16
Multiply.
Lesson 7.5
Dividing Mixed Numbers
339
Page 2 of 5
tch Out!
Wa
2
EXAMPLE
When you divide
by a mixed number, first
you rewrite it as an
improper fraction. Then
don’t forget to multiply by
the reciprocal of the
improper fraction.
3
5
1
4
Dividing by a Mixed Number
33
5
9
4
Write 6 and 2 as improper fractions.
33
5
4
9
Multiply by the reciprocal of the divisor.
3
5
6 2 11
33 4
59 3
Use the rule for multiplying fractions.
Divide out common factors.
44
15
14
15
, or 2 ✓Check
1
4
Multiply.
1
4
3
5
Round 2 to 2 and replace 6 with the compatible number 6.
The answer is reasonable because it is close to the estimate 6 2 3.
Your turn now
Divide. Use estimation to check your answer.
1
1. 9 5
6
2
8
2. 6 3
9
7
1
3. 3 8
4
1
3
4. 12 3 2
4
5. Which quotient in Exercises 1–4 is less than 1?
EXAMPLE
3
Choosing an Operation
1
Cider Forty pounds of apples make about 3 2 gallons of cider. About
how many pounds of apples are needed to make 1 gallon of cider?
Solution
1 Choose the operation by thinking about a similar whole
number problem: If 40 pounds of apples made 4 gallons
1
2
of cider, you would divide 40 by 4. So, divide 40 by 3 .
2 Divide.
1
2
40
1
7
2
40
1
2
7
40 3 40 2
17
80
7
3
7
, or 11 3
7
ANSWER You need about 11 pounds of apples to make 1 gallon of cider.
340
Chapter 7
Multiplication and Division of Fractions
Page 3 of 5
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Exercises
eWorkbook Plus
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More Practice, p. 714
Getting Ready to Practice
3
1. Vocabulary Find the reciprocal of the mixed number 2 .
8
Write the reciprocal of the divisor. Then find the quotient. Use
estimation to check your answer.
1
7
2. 5 4
8
5
2
3. 4 6
7
1
3
4. 8 3 2
4
2
5. 14 2 3
1
6. Volunteer Work If you split 5 hours of volunteer work equally over
2
the next three weeks, how much time will you volunteer each week?
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
7–8, 10–14, 22
9, 15–21, 23–27
28–31
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
7. What division problem
involving a mixed number
is represented by the model?
What is the quotient?
34
43
43
34
43
4
2
8. Sketch a model similar to Exercise 7 for 2 . Find the quotient.
5
5
2
5
9. Decide Are 3 and 3 reciprocals? Why or why not?
5
2
Find the quotient.
1
2
10. 7 5
5
2
2
11. 8 3
9
7
13
12. 4 8
16
1
13. 2 3
10
4
14. 3 5
7
5
1
15. 4 9
6
3
1
16. 2 8
4
1
17. 5 3 8
4
18. 11 2 9
1
19. 15 2 7
1
1
20. 4 2 4
2
5
1
21. 2 5 6
6
1
22. Recipes You have only a cup measure. How many times must you fill
4
1
1
the cup measure for a recipe that uses 2 cups of milk?
4
4
23. Packaging You are stacking books in a box that is 12 inches high. Each
1
book is 1 inches thick. How many books can you fit in the box in a
4
single stack?
Lesson 7.5
Dividing Mixed Numbers
341
Page 4 of 5
Estimation Estimate the quotient.
1
2
24. 15 2 3
3
9
1
25. 28 5 10
4
3
11
26. 18 1 5
12
1
27. 20 3 7
Choose the Operation Solve. Explain why you chose the operation
you used.
11
3
28. Books One book is 2 inches thick. Another book is 1 inches thick.
16
8
Will the books fit beside each other on a shelf that has a 4 inch space?
5
1
29. Twins Twin babies weigh 7 and 6 pounds. How much more does
16
2
the heavier baby weigh than the lighter baby?
30. Dog Food If a bag contains 20 cups of dog food and you feed your dog
2
2 cups per day, how many days can you feed your dog from this bag?
3
3
31. Alligators An alligator has a total length of 11 feet. The length of the
4
alligator’s tail is one half of its total length. How long is the tail?
Describe the pattern. Then find the next two numbers in the pattern.
1 1 1 1
33. , , , , _?_, _?_
2 4 8 16
1
32. 25, 5, 1, , _?_, _?_
5
4
5
Critical Thinking Predict whether the value of the expression 4 x
will be greater than 1 or less than 1 for the given value of x. Then
evaluate the expression.
2
34. x 4 5
3
35. x 5
1
37. x 5 3
36. x 6
38. Find the Error A recipe calls for
1
2 cups of broth. A cook is
3
3
making of the recipe. Describe
4
and correct any errors in finding
the amount of broth needed.
1
3
3
4
7
3
3
4
3
7
3
4
2 9
28
cup
1
1
1
39. Football Your football team gains 3 , 5, 4 , 8, and 6 yards on five
2
2
2
consecutive plays. Find the mean number of yards gained for the plays.
Evaluate the expression.
3
3
1
40. 6 1 4
8
2
342
Chapter 7
Multiplication and Division of Fractions
3
3
41. 4 5 1 10
8
1
1
6
42. 7 2 3 6
4
7
Page 5 of 5
Extended Problem Solving Talent show auditions are scheduled to
3
4
last about 3 hours. There are 31 acts to be viewed.
43. Represent Write an expression that represents the amount of time, in
hours, for one act if each act is allowed the same amount of time.
44. Estimate Use a pair of compatible numbers to estimate the value of
the expression you wrote in Exercise 43.
45. Interpret How many whole minutes should be allowed for each act?
5
8
1
2
Algebra Evaluate the expression for x and y 2 .
2x
46. y
x
48. 4y
2
47. y x
49. Challenge A movie theater is open from 12:30 P.M. to 1:00 A.M. The
1
length of each movie being shown at the theater is 2 hours. How
4
many movies can be shown on each screen during one day? Does your
answer change if there is a 15 minute break between movies? Explain.
Mixed Review
50. Use a benchmark to estimate the length of a fork in inches. Then
measure to check your estimate. (Lesson 2.1)
Find the sum or difference. (Lessons 6.4, 6.5)
4
5
51. 6 2 7
7
2
3
52. 3 4 3
4
4
53. 7 3 9
7
1
54. 5 2 10
4
Basic Skills Copy and complete the statement.
55. 5 weeks 3 days _?_ days
56. 265 min _?_ hours _?_ min
Test-Taking Practice
INTERNET
State Test Practice
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3
57. Multiple Choice If it takes you hour to read one chapter of
4
1
your book, how many chapters can you read in 5 hours?
4
15
1
B. 4 C. 6
D. 7
A. 3 16
2
1
58. Short Response How many shelves that are 1 feet long can you cut
2
3
from a board that is 4 feet long? Is there wood left over? Explain.
4
Lesson 7.5
Dividing Mixed Numbers
343