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Associative Property

Definition of Associative Property

Definition: The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.
Examples of the Associative Property for Addition
  • The picture below illustrates that it does not matter whether or not we add the 1 + 7 first (like the left side) or the 7 + 5 first, like the right side.
    Picture of Associative Property
  • Picture of Associative Property
  • (a + b) + c = a + (b + c) – Yes, algebraic expressions are also associative for addition
Examples of the Associative Property for Multiplication
  • Picture of Associative Property of Multiplication
  • Diagram of Associative Property of Multiplication
  • (a • b) •c = (a • b) •c – Yes, algebraic expressions are also associative for multiplication

Non Examples of the Associative Property

Division (Not associative)

Division is probably an example that you know, intuitively, is not associative. The examples below should help you see how division is not associative.
  • Non Example of Associative Property
Subtraction (Not associative)

Subtraction is also not associative..
  • Non Example of Associative Property