EXAMPLE 2 Writing Equivalent Expressions

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Distributive Property

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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.

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: 63 + 35 Simplify. 98 = 98 Answer checks.

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

The total cost of the lava lamps is $127.60. EXAMPLE 3 Using the Distributive Property = 128.00 – 0.40 Multiply. = 127.60 Subtract. ANSWER The total cost of the lava lamps is $127.60.

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

GUIDED PRACTICE for Examples 2 and 3 6. What If? Suppose in Example 3 that each lava lamp costs $17.90. Find the total cost of buying 6 lamps. ANSWER $107.40