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Dividing by Decimals
BEFORE
Now
WHY?
You divided by whole numbers.
You’ll divide by decimals.
So you can find the gas mileage of
a car, as in Ex. 47.
In the Real World
Pumpkins At a pumpkin patch
you choose a pumpkin weighing
9.5 pounds and pay $4.75. What is
the cost per pound of the pumpkin?
Word Watch
Review Words
dividend, p. 691
divisor, p. 691
quotient, p. 691
You will answer the question above
in Example 3. You will need to divide
by a decimal.
Dividing by a Decimal
Words When you divide by a decimal, multiply both the
divisor and the dividend by a power of ten that will
make the divisor a whole number.
1.5
.
Multiply 2.5 and 3.75 by 10.
7
.5
253
Numbers 2.53
.7
5
EXAMPLE
1
Writing Divisors as Whole Numbers
Rewrite the division problem so that the divisor is a whole number.
with
a. 1.83 2.5
Solving
When you divide by a
decimal with one decimal
place, multiply the divisor
and the dividend by 10.
For a divisor with two
decimal places, multiply
by 100, and so on.
2.51
.8
3
b. 3 0.15
Multiply the divisor
and dividend by 10.
0.153
0
0
Write zeros as
placeholders.
Multiply the divisor and
dividend by 100.
ANSWER 18.3 25
ANSWER 300 15
Your turn now
Rewrite the division problem so that the divisor is a
whole number.
1. 0.75
.6
180
Chapter 4
Decimal Multiplication and Division
2. 3.84
.5
6
3. 0.140
.8
4
4. 0.0381
7
1
Page 2 of 5
EXAMPLE
2
Using Zeros While Dividing
Find the quotient.
a. 0.88 1.6
b. 30 0.02
.
.8
8
1.60
.
0
.0
0
0.023
1500
23
0
0
0
2
10
10
0
.55
.8
0
168
8
0
80
80
0
ANSWER 0.88 1.6 0.55
EXAMPLE
Sports
3
Sometimes you need
to write zeros as
placeholders in the
quotient.
ANSWER 30 0.02 1500
Solving Problems Involving Decimals
To find the cost per pound of the pumpkin from page 180, you can divide
the total cost of the pumpkin by the number of pounds.
Divide $4.75 by 9.5 pounds.
.
9.54
.7
5
Multiply the divisor and dividend by 10.
.5
954
7
.5
47
5
0
■
Pumpkin Boat Race
In 1997, New York City
hosted the world’s first
pumpkin boat race. Only
3 pumpkin boats competed
in the 0.25 mile race. The
boats weighed 814 pounds,
787 pounds, and
752.6 pounds. What was
the mean of the weights of
the 3 boats?
ANSWER Because money is represented with two decimal places, the
pumpkin costs $.50 per pound.
✓ Check
Estimate: 4.75 9.5 ≈ 5 10 0.5. So, the answer of
$.50 per pound is reasonable.
Your turn now
5. 0.20
.9
9
Divide. Round to the nearest tenth if necessary.
6. 1.37
.6
9
7. 0.282
5
.5
8. 2.55
1
9. If you paid $10.17 for 3.4 pounds of dried fruit, what was the cost per
pound?
Lesson 4.6
Dividing by Decimals
181
Page 3 of 5
INTERNET
Exercises
eWorkbook Plus
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More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Identify the dividend and the divisor in the quotient
8.49 0.3.
Rewrite the division problem so that the divisor is a whole number.
2. 3.11
2
.8
3. 0.284
.7
6
4. 4.69
.4
3
5. 2.10
.0
4
Divide. Round to the nearest tenth if necessary.
6. 0.68
.1
7. 0.031
5
8. 0.083
2
.3
2
9. 3.26
.5
6
10. Guided Problem Solving A stack of books is 1.35 meters tall. Each
book is about 0.09 meter thick. How many books are in the stack?
1 Do you need to multiply or divide to solve the problem?
2 Write an expression to find the number of books in the stack.
3 Evaluate your expression. How many books are in the stack?
Practice and Problem Solving
Rewrite the division problem so that the divisor is a whole number.
11. 9.1 4.3
12. 14.88 0.93
13. 7 0.38
14. 15 0.2
15. 1.32 0.55
16. 17 0.24
17. 139 3.2
18. 7.67 1.3
Divide. Round to the nearest tenth if necessary.
with
Example
1
2
3
Homework
Exercises
11–18, 34
19–30, 39–46
31–33, 35–38
Online Resources
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• More Examples
• eTutorial Plus
19. 48 0.6
20. 45 1.8
21. 7.74 0.9
22. 1.18 0.2
23. 4.96 1.6
24. 20.3 0.7
25. 3.6 2.4
26. 3.48 2.4
27. 53 0.7
28. 6.2 0.7
29. 7.9 3.5
30. 199.1 5.5
Choose an Operation Solve. Explain why you chose the operation
you used.
31. Photos You have a roll of 24 pictures developed and each picture is
15.24 centimeters long. How long will the pictures be if placed
end-to-end?
32. Clothing Costs Your sweatshirt costs $29.99, your jeans cost $34.65,
and your sneakers cost $45.50. How much does your outfit cost?
33. Geometry A rectangle has an area of 43.7 square centimeters. The
length of the rectangle is 9.5 centimeters. Find the width.
182
Chapter 4
Decimal Multiplication and Division
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34. Find the Error Describe and correct the error in rewriting the problem.
0.3817
3817
0
Estimation Estimate the cost per pound of the fruit.
35. Apples: 7.1 pounds cost $7.85.
36. Bananas: 4.8 pounds cost $4.93.
37. Pears: 3.2 pounds cost $8.28.
38. Peaches: 4.5 pounds cost $6.75.
Divide. Round to the nearest tenth if necessary.
39. 0.09 3
40. 8.69 4.1
41. 40 0.05
42. 90 0.18
43. 97.2 0.9
44. 2.16 0.02
45. 21.3 0.07
46. 5.34 1.86
47. Cars Juan drives his car 470.8 miles and uses 14.5 gallons of gasoline.
Find the gas mileage (miles divided by gallons) of Juan’s car. Round
your answer to the nearest tenth.
48. Critical Thinking Why is it helpful to rewrite a division problem so that
the divisor is a whole number?
49. Writing Write an addition, a subtraction, a multiplication, and a
division problem with a solution of 3.5.
Algebra Evaluate the expression when x 4.54 and y 7.5.
Round to the nearest hundredth if necessary.
50. x y
51. y x
52. x 3.15 y
53. y x 0.8
World Population Use the table below to answer Exercises 54
and 55. Round to the nearest tenth.
Year
Population
1650
0.51
World Population (billions)
1700 1750 1800 1850 1900
0.63
0.79 0.97
1.26 1.66
1950
2.56
2000
6.08
54. How many times greater was the population in 2000 than in 1900?
55. How many times greater was the population in 1950 than in 1650?
Number Sense Copy and complete the statement using <, >, or .
56. 13.42 1.18 _?_ 134.2 118
57. 6.857 2.56 _?_ 685.7 256
58. 43.75 2.28 _?_ 43.75 22.8
59. 21.74 1.02 _?_ 21.74 0.102
Lesson 4.6
Dividing by Decimals
183
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60. Amusement Parks The average price to enter an amusement park is
$18.50. The park collects about $6.29 million just from entrance fees for
the year. About how many people visited the park?
Challenge Tell whether the statement is always, sometimes, or
never true.
61. If the divisor is less than the dividend and greater than 0, the quotient
is greater than 1.
62. If the divisor is greater than the dividend, and the dividend is greater
than 0, the quotient is less than 1.
Mixed Review
Evaluate the expression. (Lesson 1.4)
63. 15 5 2
64. 16 (2 6) 4
65. 36 23
66. Choose an appropriate customary and metric unit you might use to
measure the height of a movie screen. (Lesson 2.1)
Find the product. (Lesson 4.1)
67. 5 0.6
68. 0.02 2
69. 8.037 4
70. 0.89 21
Basic Skills The pictograph shows the results of a survey that
asked students to choose their favorite fruit. Use the pictograph to
answer the following questions.
71. Which fruit was most
popular? How many students
chose that fruit?
72. Which two fruits had the
same number of responses?
73. Find the total number of
Favorite Fruit
Apple
Orange
Banana
Watermelon
Peach
students surveyed.
5 students
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
74. Multiple Choice What is the quotient 6.56 0.4?
A. 1.64
B. 16.4
C. 164
D. 1640
75. Short Response Write a division problem that has a quotient of 2.6.
Explain how you found the divisor and the dividend.
184
Chapter 4
Decimal Multiplication and Division