Distributive Property

Definition

The distributive property of multiplication over addition:

Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

The distributive property of multiplication over subtraction:

Multiplying a difference by a number is the same as multiplying the subtrahend and the minuend by the number and then subtracting the products.

Examples

The distributive property of multiplication over addition look as follows:

3(4 + 2) = 3 × 4 + 3 × 2

3 × 6 = 12 + 6

18 = 18 (Both sides have a result of 18.)

The distributive property of multiplication over subtraction looks as follows:

3(4 − 2) = 3 × 4 − 3 × 2

3 × 2 = 12 − 6

6 = 6 (Both sides have a result of 6.)

Note

Multiplication is not distributive over multiplication.

3(4 × 2) ≠ 3 × 4 × 3 × 2

3 × 8 ≠ 12 × 6

24 ≠ 72 (Both sides do not have the same result.)

In this case the 3 needs to be distributed to the 4 or the 2, not to both.

3(4 × 2) = 3 × 4 × 2

3 × 8 = 12 × 2

24 = 24 (Both sides have a result of 24.)

3(4 × 2) = 4 × 3 × 2

3 × 8 = 4 × 6

24 = 24 (Both sides have a result of 24.)