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E#19 Name _______________________________ Date __________ Class____ SOL 5.19 - Distributive Property The distributive property states that you can multiply a sum by multiplying each addend separately, then adding their products. So… 8 x 23 = 8 x (20 + 3) = (8 x 20) + (8 x 3) = 160 + 24 = 184 Use the distributive property to solve the following equations. 1. 4 x 53 = __ x (__ + __) 2. 6 x 98 = __ x (__ + __) 3. 5 x 39 = __ x (__ + __) = (__ x __) + (__ x __) = (__ x __) + (__ x __) = (__ x __) + (__ x __) = ____ + ____ = ____ + ____ = ____ + ____ = = = 4. 7 x 26 5. 35 x 2 6. 29 x 6 7. 84 x 5 8. 73 x 7 9. 17 x 8 E#19 Simplifying with Parentheses When simplifying expressions with parentheses, you will be applying the Distributive Property. That is, you will be distributing over (multiplying through) a set of parentheses in order to simplify a given expression. The expression 3(5 + 7) is simplified as (3 x 5) + (3 x 7) When a number is next to a set of parentheses, multiply. No “x” is needed. Variables can also be used when simplifying expressions. For example: 6(n + 2) is simplified as (6 x n) + (6 x 2) TRY THESE: 8(4 + 9) = (8 x ___) + (8 x ___) 7(k + 2) = (7 x ___) + (7 x ___) Simplify the following expressions using the distributive property. 6(5 + 8) = _____________________ 2(s + 6) = _____________________ 9(n + 3) = _____________________ 4(5 + 5) = _____________________ 3(4 + 2) = _____________________ 7(t + 4) = _____________________ 5(8 + r) = _____________________ 8(5 + 3) = _____________________ E#19 Breaking Up Numbers When using the distributive property, break apart larger numbers to simplify them. For example: 6 x 53 5 x 98 6 x (50 + 3) 74 x 9 5(90 + 8) (70 + 4) x 9 TRY THESE: 8 x 56 3 x 87 4 x 23 65 x 2 8 x (___ + ___) 3(___ + ___) 4 x (___ + ___) (___ + ___) x 2 Now, simplify these equations using the distributive property. The first one is done for you! 4 x 78 3 x 87 9 x 62 8 x 34 76 x 2 32 x 5 99 x 5 53 x 4 22 x 9 = 4(70 x 8) = (4 x 70) + (4 x 8)