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What Does Associative Property of Multiplication Mean?

The Associative Property of Multiplication is one of four multiplication properties taught to students at the upper elementary level. The four properties are Commutative, Associative, Multiplicative Identity and Distributive properties. The concept behind this labeling is that students should be able to recognize and remember the basic rules of mathematical computation that apply to all real numbers. Mastering these concepts makes problems easier to solve and is one of the higher learning skills necessary to solve problems in algebra.

  1. Definition

    • The Associative Property states that when three or more numbers are multiplied, the product is the same regardless of how the factors are grouped.

    Explanation

    • When there are three or more numbers to multiply, how do you decide which ones to multiply first? How do you "associate" them? The Associative Property states that the result will be the same, no matter which two numbers you choose to multiply first.

    Example

    • Always multiply numbers in parentheses first:

      (3 x 2) x 5 = (2 x 5) x 3

      6 x 5 = 10 x 3

      30 = 30

    Further Association

    • The same concept applies to the Associative Property of Addition. When there are three or more numbers to be added, the product will be the same regardless of how the numbers are grouped.

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