6. Distributive Property There is an error in your textbook so make sure you write down the algebra and numbers part in your notes. 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 to subtraction. Algebra a(b+c) = ab + ac a(b-c) = ab - ac Numbers 6(4+3) = 6(4) + 6(3) 7(8-5) = 7(8) – 7(5)
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10. EXAMPLE 2 Using the Distributive Property = –5 x + ( –5 )(10) Distributive property = –5 x + (–50) Multiply. = 3 x + ( 3 )(8) Distributive property = 3 x + 24 Multiply. a. – 5( x + 10) b. 3( x + 8)
11. EXAMPLE 2 Using the Distributive Property = 3 (1) – 3 (20) + 3 (–5) = 3 – 60 + (–15) = 3 + (–60) + (–15) = –72 Distributive property Multiply. Add the opposite of 60 . Add. c. 3 [1 – 20 + (–5)]
12. Find the difference mentally. Find the products mentally. The mental math is easier if you think of $11.95 as $12.00 – $.05. Write 11.95 as a difference. You are shopping for CDs. You want to buy six CDs for $11.95 each. Use the distributive property to calculate the total cost mentally. 6( 11.95 ) = 6( 12 – 0.05 ) Use the distributive property. = 6( 12 ) – 6( 0.05 ) = 72 – 0.30 = 71.70 S OLUTION The total cost of 6 CDs at $11.95 each is $71.70.
