Distributive and Commutative Properties

You are now very familiar with the four operations: addition, subtraction, division, and multiplication.  With multiplication, there is a property called distribution, where a factor can be multiplied across a sum of numbers before adding the numbers.  Both multiplication and addition are commutative operations i.e. it doesn’t matter which order you choose to multiply or add the numbers: the final result will always be the same.  We see examples of these properties below: 

Distributive Property: 

5 x (3 + 2) = 5(3 + 2) = 15 + 10 = 25 

5 x (3 + 2) = 5 x 5 = 25  

Commutative Property: 

2 + 3 + 7 = 12 

3 + 7 + 2 = 12 

7 + 2 + 3 = 12 

5 x (3 x 2) = 5 x 6 = 30 

(5 x 3) x 2 = 15 x 2 = 30 

(5 x 2) x 3 = 10 x 3 = 30 

As seen above, the distributive and commutative properties make simplifying mathematical expressions involving multiplication and addition easier and will give the same results.