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The Associative Property

Written by tutor Anicia H.

What word comes to mind when you hear “associative?” It comes from “to associate, to be grouped together.” Parentheses show the association and the operations in the parentheses are performed first. Notice that the order of the numbers does not change – only the grouping. The associative property becomes important because it allows the mathematician, you, to add or multiply numbers with ease. When you follow the examples below it will become clear how the associative property is used. The associative property can only be used for addition and multiplication, not for subtraction or division.

The Associative Property of Addition

Example 1: (14 + 6) + 7 = 14 + (6 + 7)

Adding 14 + 6 easily gives the sum of 20 to which we can add 7. The right hand side of the equation is where we add 14 and 13. Both sides will result in 27.

Example 2: (52 + 7) + 13 = 52 + (7 + 13)

Adding 7 + 13 on the right side of the equation is easier than adding 52 + 7 on the left. We still get the final result of 72.

The Associative Property of Multiplication

Similar examples can illustrate how the associative property works for multiplication.

Example 3: (3 * 5 ) * 6 = 3 * (5 * 6)

Now which side of the equation is easier for you? Most often, it is 5 * 6 on the right side.

Example 4: 2 * (18 * 10) = (2 * 18) * 10

Here the left side is written differently, yet you can still see how the associative property makes the multiplication on the left side easier.

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