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The Distributive Property
Goal: Evaluate expressions using the distributive property.
Vocabulary
Equivalent expressions:
Distributive property:
EXAMPLE
1
Two expressions that are equal in value
are equivalent expressions.
For all numbers a, b, and c,
a(b c) ab ac and a(b c) ab ac.
Writing Equivalent Expressions
Tea Party A tea party has two rectangular tables: one that is 6 feet by
5 feet, and one that is 6 feet by 4 feet. What two expressions could be
used to find the total area of the tables?
Solution
6
5
6
ft
ft
4
6
ft
ft
Area 6(5) 6(4)
30 24 54 ft2
(
5
4
)
ft
ft
Area 6(5 4)
6(9) 54 ft2
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)
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Chapter 6
Notetaking Guide
EXAMPLE
2
Writing Equivalent Expressions
Use the distributive property to write an equivalent expression.
Check your answer.
a. 6(2 7)
b. 3(75 25)
c. 8(2) 8(9)
Solution
6(2 7) 6(2) (6)(7)
a.
Distributive property
Check: 6(9) 12 (42)
Simplify.
54 54 ✓
b.
Answer checks.
3(75 25) 3(75) 3(25)
Distributive property
Check: 3(50) 225 75
Simplify.
150 150 ✓
Answer checks.
8(2) 8(9) 8(2 9)
c.
Distributive property
Check: 16 72 8(11)
Simplify.
88 88 ✓
Guided Practice
Answer checks.
Use the distributive property to write an equivalent
expression. Check your answer.
14 34 1. 5 5 14
2. 4(7 5)
3
4
5 3. 9(15 8)
4(7) (4)(5)
4. 10(6) 10(2)
9(15) 9(8)
10(6 2)
Lesson 6.7
The Distributive Property
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EXAMPLE
3
Using the Distributive Property
Scrapbooks Leslie is making a scrapbook for her mother’s birthday. She
bought 6 packs of stickers for $6.95 each. Use the distributive property
to find the total cost of the stickers.
Solution
6(6.95) 6(7.00 0.05)
Write 6.95 as a difference of
a whole number and a decimal.
6(7.00) 6(0.05)
Distributive property
42.00 0.30 41.70
Multiply. Then subtract.
Answer: The total cost of the stickers is $ 41.70 .
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Chapter 6
Notetaking Guide