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 =?

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

Then multiply each part by x 5 =? 40 3 x 5 x

Finally, sum your two products 43 x 5 = x 5 x = 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 = ?

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

Multiply each part by x 6 = ? 50 3 x 6 x

Sum the two products. 53 x 6 = x 6 x = 318 +

Example 1 5(3 + 2) Proof: 5(3+2) = 5(5) = = 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 (5 + x)= x 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)