Distributive Property of Real Numbers

The distributive property connects the operations of multiplication and addition or subtraction. It tells us how to simplify expressions where a number is multiplied by a group of terms.

Expressions

Distributivity of multiplication over addtion.

$a(b + c) = ab + ac$

Distributivity of multiplication over subtraction.

$a(b - c) = ab - ac$

In formal terms:

$\forall a, b, c \in \mathbb{R},\ a \cdot (b + c) = a \cdot b + a \cdot c$

$\forall a, b, c \in \mathbb{R},\ a \cdot (b - c) = a \cdot b - a \cdot c$

Examples

$2(3 + 4) = 2 \cdot 3 + 2 \cdot 4 = 6 + 8 = 14$
$5(10 - 2) = 5 \cdot 10 - 5 \cdot 2 = 50 - 10 = 40$

True or False Activity!!!

Read each statement carefully and decide if it is true or false.

The distributive property allows us to multiply a number by a sum or difference.

The distributive property only works with addition.

Distributivity only applies to multiplication over addition or subtraction.

a(b + c) = ab + c is an example of the distributive property.

Build the Distributive Equations

Build the Correct Equations Activity

Distributive Property over Addition

Distributive Property over Subtraction

End of Lesson