Download Dividing Fractions and Mixed Numbers

Page 1 of 5
Dividing Fractions
and Mixed Numbers
BEFORE
Now
WHY?
You multiplied fractions and
mixed numbers.
You’ll divide fractions and
mixed numbers.
So you can set up a slalom skiing
course, as in Ex. 35.
1
4
You can use a model to find the quotient 2 .
Word Watch
reciprocal, p. 222
First draw two unit squares. Then divide
each square into fourths.
1
4
There are 8 fourths in the model. So, 2 8. Notice that there are
4 fourths in each square and there are 2 squares, so 2 4 8. The
1
4
numbers and 4 are reciprocals. Two nonzero numbers whose product
is 1 are reciprocals .
2
3
2 3
and are reciprocals, because p 1.
3
2
3 2
1
5
1
5
5 and are reciprocals, because 5 p 1.
1
4
As you saw above, 2 2 4, which suggests the following rule.
Using Reciprocals to Divide
Words To divide by any nonzero number, multiply by its
reciprocal.
3
2
3 3
9
Numbers p 4
3
4 2
8
c
a
a d
ad
Algebra p d
b
b c
bc
(b, c, d 0)
EXAMPLE
1
5
2
5 3
p 9
3
9 2
5p31
9p2
3
5
6
222
Chapter 5
Fraction Operations
Dividing a Fraction by a Fraction
Multiply by reciprocal.
Use rule for multiplying fractions.
Divide out common factor.
Multiply.
Page 2 of 5
with
Solving
In Example 2, you can
check your answer by
multiplying the quotient
and the divisor and
comparing the result
with the dividend:
2
2
2
4
2 .
5
5
1
5
2
EXAMPLE
Dividing a Fraction by a Whole Number
4
4 1
2 p 5
5 2
2
4p1
5p2
Multiply by reciprocal.
1
2
5
Use rule for multiplying fractions.
Divide out common factor.
Multiply.
Your turn now
Find the quotient. Simplify if possible.
5
7
1. 6
9
EXAMPLE
9
3
2. 2
2
3
1
3. 3
6
2
4. 4
3
Drawing a Diagram to Solve a Problem
In-line Skating You set up an in-line skating course 21 feet long to
1
2
practice weaving around cones. You want a cone every 3 feet, but not
at the start or end of the course. How many cones will you need?
Solution
Method 1 Draw a diagram on graph paper. Make the course 21 grid boxes
1
2
long. Draw a point to mark the location of a cone every 3 grid boxes.
Method 2 Use division.
1
2
7
2
Write 3 as an improper fraction.
2
7
Multiply by reciprocal.
21 3 21 21
1
3
21 2
17
1
6
1
2
Use rule for multiplying fractions.
Divide out common factor.
Multiply.
1
2
The quotient 6 gives you the number of 3 foot spaces, not the number
of cones. You have to subtract 1 to get the number of cones: 6 1 5.
ANSWER You will need 5 cones.
Lesson 5.4
Dividing Fractions and Mixed Numbers
223
Page 3 of 5
EXAMPLE
with
3
4
Solving
4
5
8
Dividing Two Mixed Numbers
35
4
21
8
3
4
8 2 In Example 4, you can
estimate the answer by
rounding each mixed
number to the nearest
whole number. By doing
so, you have 9 3 3,
so the answer is reasonable.
35
4
8
21
p 5
35 p 8
4 p 21
1
10
3
Multiply by reciprocal.
2
Use rule for multiplying fractions.
Divide out common factors.
3
1
3
, or 3 Your turn now
6
5. 3 11
5
8
Write 8 and 2 as improper fractions.
Multiply.
Find the quotient. Then estimate to check the answer.
2
6. 12 2 5
2
3
7. 5 3
5
1
1
8. 4 1 2
4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 709
Getting Ready to Practice
3
1. Vocabulary Copy and complete: The reciprocal of is _?_.
7
2. Writing Explain in your own words how to divide a fraction by a fraction.
Write the reciprocal of the number.
1
3. 7
4. 8
4
5. 1 9
3
6. 3 4
Match the division expression with the related multiplication
expression.
4
3
7. 9
20
7
3
8. 8
13
1
1
9. 1 4 7
3
3
8
A. 7
13
3
9
B. 20
4
20
4
C. 3
9
2
1
10. 6 2 3
4
7
13
D. 8
3
11. Sandwiches To surprise the guests at a party, the host prepares a
1
5 foot long submarine sandwich. The sandwich is cut into 11 equal
2
pieces. How long is each piece?
224
Chapter 5
Fraction Operations
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
16–27
16–27
35–36
16–27
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Write the reciprocal of the number.
5
12. 6
3
13. 1 4
2
14. 5 5
15. 1
Find the quotient. Then check the answer.
3
1
16. 8
4
5
6
17. 14
7
2
8
18. 1 15
9
7
19. 4
12
9
20. 6
10
3
21. 8 2 4
1
22. 10 4 6
3
1
23. 4 10
5
5
24. 2 7
6
2
25. 5 3
1
4
26. 9 1 13
5
7
1
27. 7 2 12
6
5
8
Algebra Evaluate the expression when x and y 3.
28. x y
1
30. 4 y
6
29. y x
31. Cooking Making pasta requires boiling 6 cups of water, but your
1
measuring cup holds only 1 cups. How many times do you need
2
to fill the measuring cup?
Evaluate the expression.
9
3
5
32. 2 3 3 10
5
8
2
1
3
33. 5 3 8 3
2
5
2
2
3
34. 6 3 5 7
3
4
35. Slalom Skiing On a slalom skiing course, the distance from the start
to the first gate is 15 meters, and the distance from the last gate to
the finish is 20 meters. If the slalom course is 635 meters long and
1
2
the distance between gates is 1 meters, how many gates are needed
for the course?
36. Draw a Diagram You are an editor for your school yearbook. Each
5
row of photos is 8 inches wide, including the margins. Each photo is
8
1
1
1 inches wide, the space between each photo is inch, and each
4
8
1
margin is inch. How many photos can fit in one row?
4
37. Challenge Choose a nonzero number and divide it by a series
3 2 1
of fractions, each less than the one before, such as , , , . . . .
4 3 2
Describe what happens to the corresponding series of quotients.
Lesson 5.4
Dividing Fractions and Mixed Numbers
225
Page 5 of 5
Mixed Review
In Exercises 38 and 39, copy and complete the statement using
the appropriate metric unit. (Lesson 2.6)
38. The capacity of a vase is 325 _?_.
39. A basketball has a mass of 0.62 _?_.
5
3
40. Find the product of and 7 . (Lesson 5.3)
12
5
Basic Skills Use a ruler to draw a segment with the given length.
41. 5 inches
1
42. 3 inches
2
3
43. inch
4
5
44. 2 inches
8
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
3
45. Extended Response A CD case is inch wide. A cassette case is
8
5
inch wide. If you want to put 8 cassettes on a shelf that is
8
20 inches wide, how many CDs would fit in the remaining space?
Explain your reasoning.
Mix and Match
Play this game with a partner. Take turns doing the following:
1. Choose two fractions from the clothesline. (Fractions cannot be used more than once.)
2. Let one fraction be the dividend and the other be the divisor.
3. Find the quotient. (Your partner should check your answer.)
4. Add the quotient to your score. (You both start with a score of zero.)
Once all the fractions have been used, the player with the higher score wins.
226
Chapter 5
Fraction Operations