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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) Distributive property = ? –20 + (–32) Check: –4(13) Simplify. –52 = –52 Answer checks.

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**EXAMPLE 2 b. Expression: 4(50 – 3) = 4(50) – 4(3) = ? 200 – 12 Check:**

Writing Equivalent Expressions b. Expression: 4(50 – 3) = 4(50) – 4(3) Distributive property = ? 200 – 12 Check: 4(47) Simplify. 188 = 188 Answer checks. c. Expression: 7(9) + 7(5) = 7(9 + 5) Distributive property = ? 7(14) Check: Simplify. 98 = 98 Answer checks.

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EXAMPLE 3 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 $ Use the distributive property to find the total cost of the lamps. SOLUTION 8(15.95) = 8(16.00 – 0.05) Write as a difference of a whole number and a decimal. = 8(16.00) – 8(0.05) Distributive property

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**The total cost of the lava lamps is $127.60.**

EXAMPLE 3 Using the Distributive Property = – 0.40 Multiply. = Subtract. ANSWER The total cost of the lava lamps is $

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GUIDED PRACTICE for Examples 2 and 3 Use the distributive property to write an equivalent expression. Check your answer. ( ) + 6( ) 1 7 6 (12 – 5) ANSWER 6( ) 1 7 6 ANSWER 8(12) – 8(5) 3. – 6(12 + 3) (11) – 3(4) ANSWER – 6(12) + (– 6)(3) ANSWER 3(11 – 4)

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GUIDED PRACTICE for Examples 2 and 3 6. What If? Suppose in Example 3 that each lava lamp costs $ Find the total cost of buying 6 lamps. ANSWER $107.40

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