Associative Property

The property that states that the way addends are grouped or factors are grouped does not change the
sum or the product

Examples:

sum   12 + (5 + 9) = (12 + 5) + 9

product   (9 x 8) x 3  =  9 x (8 x 3)

(3 + 4) + 2 = 9              3 + (4 + 2) = 9
             Think: "grouping."
 

 

 

Associative Property of Addition
The property that states that the way addends are grouped does not change the sum

Example:

(5 + 9) + 3 = 5 + (9 + 3)
       14 + 3 = 5 + 12
             17 = 17


Associative Property of Multiplication
The property that states that the way factors are grouped does not change the product

Example:

(2 x 3) x 4 = 2 x (3 x 4)
        6 x 4 = 2 x 12
            24 = 24
 

Changing the grouping of the factors does not change the product.

(5 x 0) x 4 = 0           5 x (0 x 4) = 0
             Think: "grouping."


Example

(2 x 3) x 1 = 2 x (3 x 1)

        6 x 1 = 2 x 3

              6 = 6