The Associative Property in Math

According to the associative property, the addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property involves three or more numbers. The parentheses indicate the terms that are considered one unit. The groupings are within the parenthesis—hence, the numbers are associated together.

In addition, the sum is always the same regardless of how the numbers are grouped. Likewise, in multiplication, the product is always the same regardless of the grouping of the numbers. Always handle the groupings in the brackets first, according to the order of operations.

Addition Example

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The Associative and Commutative Properties

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When you change the groupings of addends, the sum does not change:

(2 + 5) + 4 = 11 or 2 + (5 + 4) = 11
(9 + 3) + 4 = 16 or 9 + (3 + 4) = 16

When the grouping of addends changes, the sum remains the same.

Multiplication Example

When you change the groupings of factors, the product does not change:

(3 x 2) x 4 = 24 or 3 x (2 x 4) = 24

When the grouping of factors changes, the product remains the same just as changing the grouping of addends does not change the sum.