Associative Properties

The Associative Properties deal with adding and multiplying when there are three terms.

Associative Property of Addition:

(a + b) + c = a + (b + c)

Associative Property of Multiplication:

(a x b) x c = a x (b x c)

To use the Associative Properties correctly, you need to follow the order of operations and solve the portions in parentheses first.

Just change the order of the terms you are adding or multiplying.

Example math problems related to associative properties:

  1. (3 + 4) + 12 = 3 + (4 + 12)
    • (7) + 12 = 3 + (16)
    • 19 = 19
  2. (1 + 14) + 6 = 1 + (14 + 6)
    • (15) + 6 = 1 + (20)
    • 21 = 21
  3. (5x)y = 5(xy)
    • 5xy = 5xy
  4. 3(5 x 7) = (3 x 5)7
    • 3(35) = (15)7
    • 105 = 105
  5. (mn)y = m(ny)
    • mny = mny

Note – Parentheses ( ) means to multiply.

It’s important to recognize that the Associative Property works for adding and multiplying, but not for dividing and subtracting.