Math 6 Honors Periods 1, 6 & 7

The Distributive Property 1-4

Distributive Property of Multiplication
(with Respect to Addition)

For any whole numbers a, b, and c,

a x (b + c) = (a x b) + (a x c)
and (b + c ) x a = (b x a ) + (c x a)

or written without the multiplication operator symbol
a(b + c) = ab + ac
(b+c)a = ba + bc
Remember that the parentheses indicate which operation to do first.


How could we simplify the following using the distributive property?

a. 13 x 15
13(10 + 5) = 13(10) + 13(5)


b. (11 x 4) + (11 x 6)
11( 4 + 6) = 11(10)

Distributive Property of Multiplication
(with Respect to Subtraction)

For any whole numbers a, b, and c,

a x (b - c) = (a x b) - (a x c)
and (b - c ) x a = (b x a ) - (c x a)

or written without the multiplication operator symbol

a(b -c) = ab - ac
(b-c)a = ba - ca which is better written ab- ac

Since multiplication is distributive with respect to both addition and subtraction, we refer to both properties as the distributive property.