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The Distributive Property
BEFORE
Now
You used order of operations
to evaluate expressions.
You’ll use the distributive
So you can find the cost of a field
property to evaluate expressions. trip, as in Ex. 6.
WHY?
In the Real World
Word Watch
distributive property, p. 159
Car Wash Your class held a two-day
car wash to raise money. The class
washed 40 cars on the first day and
30 cars on the second day. The class
charged $5 for each car. How much
money did the class raise?
EXAMPLE
1
Evaluating Expressions
Method 1 To answer the question above, first find the total number
of cars washed. Then multiply to find the total amount raised.
with
Review
Charge per car Total number of cars washed 5(40 30)
5(70)
Remember that 5(70) is
another way to write 5 70.
350
Method 2 To answer the question above, first find the amount raised
each day. Then add to find the total amount raised.
First day amount Second day amount
5 40 5 30
200 150
350
ANSWER Your class raised $350.
The methods used in Example 1 show the distributive property .
The Distributive Property
Words You can multiply a number and a sum by multiplying
the number by each part of the sum and then adding these
products. The same property applies with subtraction.
Numbers 3(4 6) 3(4) 3(6)
2(8 5) 2(8) 2(5)
Algebra a(b c) ab ac
a(b c) ab ac
Lesson 4.2
The Distributive Property
159
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EXAMPLE
2
Using the Distributive Property
a. 2(50 6) 2(50) 2(6)
100 12
86 24
112
62
Your turn now
Use the distributive property to evaluate.
1. 2(17 10)
EXAMPLE
b. 10(8.6 2.4) 10(8.6) 10(2.4)
2. 7(20 3)
3
3. 100(6.8 4)
4. 0.5(24 18)
Evaluating Using Mental Math
a. To find 6(87), rewrite 87.
b. To find 8(6.1), rewrite 6.1.
6(87) 6(90 3)
8(6.1) 8(6 0.1)
6(90) 6(3)
8(6) 8(0.1)
540 18
48 0.8
522
48.8
Science
EXAMPLE
4
Using a Formula
Astronomy The Hubble Telescope orbits Earth at a rate of about
4.78 miles per second. How far does the telescope travel in 3 seconds?
Solution
Use the formula Distance Rate Time.
Distance (4.78)3
■
Astronomy
The Hubble Space Telescope
is a satellite that takes
photographs of outer space
and sends them to Earth. The
telescope was launched on
April 24, 1990. Traveling at
about 5 miles per second,
how far does the telescope
travel in 1 day? in 1 year?
160
Chapter 4
Use 4.78 for the rate and 3 for the time.
(5 0.22)3
Rewrite 4.78 as 5 0.22.
(5)3 (0.22)3
Use the distributive property.
15 0.66
Multiply.
14.34
Subtract.
ANSWER The telescope travels about 14.34 miles in 3 seconds.
Your turn now
Use mental math to find the product.
5. 8(53)
Decimal Multiplication and Division
6. 4(97)
7. 3(12.8)
8. 7(1.4)
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INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Rewrite the expression 2(3.1 7.4) using the distributive
property.
Copy and complete the statement using the distributive property.
2. 3(40 5) 3(_?_) _?_(5)
3. 7(50 2) 7(_?_) _?_(2)
4. 6(7 5.4) 6(_?_) _?_(5.4)
5. 8(3.2 9) 8(_?_) _?_(9)
6. Field Trip A class of 30 students is taking a field trip to a museum.
The cost for each student is $9 for admission plus $5 more for the
laser show. How much money is needed to pay for all the students
to see the museum and the laser show?
Practice and Problem Solving
Use the distributive property to evaluate the expression.
7. 4(80 3)
8. 6(7 50)
9. 2(39 10)
11. 6(8.2 3)
12. 8(3.1 5.7)
13. 10(4.8 2.7) 14. 14(8.1 6)
15. 3(90 0.6)
16. 9(7 0.11)
17. 7(13 0.02)
19. Find the Error Describe and
10. 15(2 9)
18. 12(3 0.4)
2(32 6) 2(32) 6
correct the error in the solution.
64 6
70
with
Example
1
2
3
4
Homework
Exercises
7–18, 33
7–23
22–32
33, 37
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Copy and complete the statement.
20. 5(30 0.2) 5(30) _?_(0.2)
21. 7(40 8) _?_(40) _?_(8)
22. 4(7.9) 4(8 _?_)
23. 3(67) 3(_?_ 7)
Use the distributive property and mental math to find the product.
24. 6(37)
25. 7(98)
26. 3(85)
27. 9(41)
28. 8(5.7)
29. 5(9.2)
30. 9(7.3)
31. 7(6.9)
32. Find the product 7(2.006) using the distributive property.
33. Lunch Costs For each day of school, you pay $2.50 for lunch
and $.45 for milk. How much money do you spend in 5 days?
Lesson 4.2
The Distributive Property
161
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U.S. Mint In Exercises 34–36, use the table. It shows what it cost
to produce some U.S. coins in two different years.
Currency
34. Evaluate the expression 50(2.0 1.6) to
find how much more it cost to produce
50 dimes in 2000 than in 1995.
35. Evaluate the expression 50(0.8 0.7) to
find how much more it cost to produce
50 pennies in 2000 than in 1995.
Coin
Penny
Nickel
Dime
Quarter
1995
0.7¢
2.74¢
1.6¢
3.65¢
2000
0.8¢
3.0¢
2.0¢
5.0¢
36. Write an expression to find how much more it cost to produce
50 nickels in 2000 than in 1995. Then evaluate the expression.
37. Geometry Use the formula P 2(l w) to find the perimeter of a
flower box with length 27 inches and width 6 inches.
■
Algebra Use the distributive property to rewrite the expression.
For example, 2(x 4) 2x 8.
U.S. Mint
Coins are minted in
Philadelphia and in Denver.
Coins minted in Denver have
a “D” on the front. Coins
minted in Philadelphia have a
“P” on the front. Do you think
people in your class have
coins from Denver or
Philadelphia? Why?
38. 3(x 7)
39. 5(x 5.2)
40. 6(4 x)
Challenge Rewrite the expression as a product using parentheses.
41. 4x 4y
42. 0.9m 0.9n
43. 5.5x 5.5y 5.5
Mixed Review
Order the numbers from least to greatest. (Lesson 3.3)
44. 2.1, 2.9, 2.8, 2.6
45. 7.63, 7.06, 7.61, 7.6
46. 0.5, 0.55, 0.05, 0.005
Evaluate the expression when x 3.1 and y 5.62. (Lesson 3.6)
47. x 2.83
48. x y
49. y 3.092
Basic Skills Round to the place value of the red digit.
50. 63,498
51. 32,921
52. 204,238
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
53. Multiple Choice Which expression is equal to 4(2 6)?
A. 2(4 6)
B. 4 2 6
C. 4 2 6
D. 4 2 4 6
54. Multiple Choice Which expression is equal to 2(4.9)?
F. 2(4 9)
162
Chapter 4
Decimal Multiplication and Division
G. 2(4 0.9)
H. 2 4 9
I. 2(5 1)