Distributive Property

The Distributive Property of Multiplication over Addition

The distributive property comes in handy when mentally multiplying numbers and in algebraic calculations.

The problem is, it's a bit tricky to explain in words:

The distributive property says you can multiply a sum by multiplying each addend separately and then add the products.

Here is what it means using numbers:

Take this mathematical expression 25 x 7 Break apart one factor into 2 addends (20 + 5) x 7 Multiply each of the addends by the other factor (20 x 7) + (5 x 7)

The property gets its name because, in this case, the 7 is "distributed" to both the 20 and the 5.

An array can be used to demonstrate why the distributive property works. A 13 x 6 array can be split into two parts: a 10 x 6 array and a 3 x 6 array. Of course there are the same number of squares in both pictures below, so 13 x 6 = (10 x 6) + (3 x 6).

The distributive property works with subtraction as well. This is helpful when doing math mentally, as in the example below.

6 x 99 = 6 x (100-1) = (6 x 100) - (6 x 1)