# The Distributive Property. The distributive property is mental math strategy that can be used when multiplying. 43 x 5 =?

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The Distributive Property

The distributive property is mental math strategy that can be used when multiplying. 43 x 5 =?

Break apart the double-digit number. 43 x 5 =? 40 3 +

Then multiply each part by 5. 43 x 5 =? 40 3 x 5 x 5 +

Then multiply each part by 5. 43 x 5 =? 40 3 x 5 x 5 200 15 +

Finally, sum your two products 43 x 5 =215 40 3 x 5 x 5 200 15 += 215 +

Let’s look at another example. 53 x 6 = ?

Break apart the double-digit number. 53 x 6 = ?

Break apart the double-digit number. 53 x 6 = ? 50 3 +

Multiply each part by 6. 53 x 6 = ? 50 3 x 6 x 6 +

Multiply each part by 6. 53 x 6 = ? 50 3 x 6 x 6 300 18 +

Sum the two products. 53 x 6 = 318 50 3 x 6 x 6 300 + 18 = 318 +

Example 1 5(3 + 2) Proof: 5(3+2) = 5(5) = 25 15 + 10= 25

D.P. with Addition 3(x + 2) = Use the Distributive Property: 3(x) + 3(2)= Now multiple: 3x + 6 This your answer

Practice 2(x + 5)= 2(5 + x)= x(2 +5)=

Answers 2(x + 5)= 2x + 10 2(5 + x)= 10 + 2x x(2 +5)= 2x + 10

D.P. with Subtraction Example: Apply the Distributive Property 3(1 –y)= Multiply, and keep the subtraction sign 3(1) – 3(y) Your answer 3 – 3y

Practice 2(x –5) = 3(5 –x) = (x –5)3 =

Answers 2(x –5) = 2x -10 3(5 –x) = 15 -3x (x –5)3 = 3x -15

Your Turn Use the distributive property to rewrite the expression without parenthesis 1.3(x + 4) 2.- (y – 9) 3.x(x + 1) 4.2(3x – 1) 5.(2x – 4)(-3)

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