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The Distributive Property
BEFORE
Now
WHY?
You evaluated expressions
using order of operations.
You’ll evaluate expressions
using the distributive property.
So you can find the cost of trading
cards, as in Ex. 21.
In the Real World
Word Watch
equivalent expressions,
p. 288
distributive property,
p. 288
Theater To form two walls for a scene
in the play The Miracle Worker, a set
designer joins a rectangle of plywood
with a width of 4 feet and a length of
6 feet to a rectangle with a width of
3 feet and a length of 4 feet. The set
designer needs to know the total
area of the two pieces in order to
purchase wallpaper. What two
expressions could be used to find
the total area of the pieces?
EXAMPLE
1
Writing Equivalent Expressions
You can find the total area by finding the sum of the areas of the
separate walls or by finding the area of the walls joined together.
4
3
4
4
6
Area 4(3) 4(6)
12 24 36
(3 6)
Area 4(3 6)
4(9) 36
Both expressions in Example 1 are equal to 36. Because the two
expressions have the same value, they are called equivalent expressions .
These expressions are an example of the distributive property .
The Distributive Property
Algebra For all numbers a, b, and c, a(b c) ab ac
and a(b c) ab ac.
Numbers 8(10 4) 8(10) 8(4) and 3(4 2) 3(4) 3(2)
288
Chapter 6
Integers
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EXAMPLE
2
Writing Equivalent Expressions
Use the distributive property to write an equivalent expression.
Check your answer.
a. 4(5 8)
b. 4(50 3)
c. 7(9) 7(5)
Solution
a. Expression: 4(5 8) 4(5) (4)(8)
4(13) 20 (32)
Check:
with
The symmetric property of
equality lets you read an
equation from left to right
or from right to left, so if
a(b c) ab ac, then
ab ac a(b c).
Simplify.
52 52 ✓
Solving
Answer checks.
b. Expression: 4(50 3) 4(50) 4(3)
Distributive property
4(47) 200 12
Check:
Simplify.
188 188 ✓
Answer checks.
c. Expression: 7(9) 7(5) 7(9 5)
Distributive property
63 35 7(14)
Check:
Distributive property
Simplify.
98 98 ✓
Answer checks.
Your turn now
Use the distributive property to write an equivalent
expression. Check your answer.
1
6
1. 6 6 7
7
EXAMPLE
3
2. 6(12 3)
3. 8(12 5)
4. 3(11) 3(4)
Using the Distributive Property
Lava Lamps You are buying 8 small lava lamps as door prizes for a disco
party that your school is having. Each lava lamp costs $15.95. Use the
distributive property to find the total cost of the lamps.
Solution
Write 15.95 as a difference of
a whole number and a decimal.
8(15.95) 8(16.00 0.05)
8(16.00) 8(0.05)
Distributive property
128.00 0.40 127.60
Multiply. Then subtract.
ANSWER The total cost of the lava lamps is $127.60.
Lesson 6.7
The Distributive Property
289
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 710
Getting Ready to Practice
1. Vocabulary Copy and complete: You can use the distributive property
to write _?_ expressions.
Match the expression with an equivalent expression.
2. 3(4 3)
3. 3(4 3)
4. 4(3 3)
5. 4(3 3)
A. 4(3) 4(3)
B. 3(4) 3(3)
C. 4(3) 4(3)
D. 3(4) 3(3)
6. Find the Error Describe and
8(5 4) 40 32
correct the error in using the
distributive property to evaluate
the expression 8(5 4).
12
7. Pumpkins You buy 2 pumpkins to carve for
Halloween. The pumpkins weigh 10 pounds
and 6 pounds, and cost $.70 per pound.
Use the distributive property to write two
equivalent expressions to represent the total
amount that you pay for the pumpkins.
Practice and Problem Solving
Use the distributive property to write an equivalent expression.
Check your answer.
8. 5(3 7)
9. 4(4 5)
10. 7(3) 7(4)
5
1
12. 6 6 12
12
11. 8(100 4)
3
2
13. 4 4 5
5
Use the distributive property to evaluate the expression.
14. 3(7.3) 3(2.7)
with
Example
1
2
3
Homework
Exercises
8–19, 25
8–19
21–22
3
4
18. 13 13 7
7
19. 3(10.4)
each individual in a group. How can this meaning help you remember
the distributive property?
21. Trading Cards A friend is selling his collection of trading cards. He is
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selling each card for $.95, and you want to purchase 20 cards. Write an
expression for the total cost of 20 cards. Then use the distributive
property and mental math to evaluate the expression.
• More Examples
• eTutorial Plus
Chapter 6
16. 9(13.2) 9(6.8)
20. Writing One meaning of the word distribute is to supply or deliver to
Online Resources
290
5
3
17. 11 11 8
8
15. 4(8.1) 4(2.9)
Integers
Page 4 of 4
22. Talent Show At a talent show, each performer has 2 minutes to set up,
3 minutes for an introduction, and 5 minutes for the act. There are
20 people performing. How long will the talent show be in minutes?
Algebra Use the distributive property to find the missing number
or variable.
23. n p 30 n p 40 n(30 _?_ )
24. 18 p 4 18 p _?_ 18(4 a)
25. Quilting A rectangular section of a quilt is made up of two smaller
rectangles. The larger of the two rectangles is 8 inches long and
4 inches wide. Its dimensions are twice the dimensions of the smaller
rectangle. Write two equivalent expressions for the area of the entire
quilt section.
26. Technology You want to find the product 5 215, but the “2” button
on your calculator is broken. How can you use the distributive property
and your calculator to find the product?
27. Challenge The expression 2l 2w is used to find the perimeter of
a rectangle. Use the distributive property to write an equivalent
expression for the perimeter. Show that both formulas work for finding
the perimeter of a rectangle that is 14 cm long and 12 cm wide.
Mixed Review
Order the integers from least to greatest. (Lesson 6.1)
28. 4, 4, 3, 3, 5, 6
29. 7, 8, 9, 10, 5, 8, 9
Order the rational numbers from least to greatest. (Lesson 6.6)
1
2
8
30. , 0.2, , , 2
2
5
7
22
21
16
31. , 5, , , 4.8
5
4
3
Basic Skills Use a ruler to draw a segment with the given length.
1
32. inch
4
3
33. inch
4
5
34. 1 inches
16
7
35. inch
16
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
36. Multiple Choice What is the value of the expression 9(7 2)?
A. 81
B. 65
C. 61
D. 45
37. Multiple Choice Which expression represents the perimeter of
a rectangle with a width of 2 units and a length of 7 units?
F. 2 p 5 2
G. 5(2 2)
H. 2(7 2)
Lesson 6.7
I. 2(2 5)
The Distributive Property
291