Commutative and associative properties

As you have seen in our math classes, we've been studying the properties of numbers. So, let's take a look at them:

• The Commutative Property of Addition and Multiplication

3 + 2 = 2 + 3

(5 = 5)

3 x 6 = 6 x 3

(18 = 18)

If you change the order of the numbers, the results won't change.

Remember: You can only use the Commutative Property with Addition or Multiplication. Don't use it with Subtraction or Division.

• The Associative Property of Addition and Multiplication

(2 + 3) + 7 = 2 + (3 + 7)

(5) + 7 = 2 + (10)

12 = 12

(2 x 3) x 4 = 2 x (3 x 4)

(6) x 4 = 2 x (12)

24 = 24

Moving the parentheses will not affect the results.

Let's Practice

Use the commutative property to solve the equations:

a) 2 x 3 x 2 = 2 x 2 x 3

b) 3 + 4 + 12 = 3 + 12 + 4

c) 32 x 2 = 2 x 32

d) 44 + 3 + 15 = 44 + 15 + 3

 

 

Now use the associative property to solve:

a) (123 + 3) + 23 = 123 + (3 + 23)

b) (9 x 8) x 2 = 9 x (8 x 2)