The associative property states that regrouping three or more whole numbers does not change the sum or product: and . It supports choosing convenient groupings to compute efficiently and distinguishes regrouping from changing the order of numbers, which is the commutative property; more general treatment with other number systems is not included here.
The associative property lets you regroup three or more whole numbers without changing the answer. The numbers stay in the same order; only the parentheses change.
For addition:
Find:
Group the numbers that are easy to add. Since , regroup the expression:
Add inside the parentheses first:
So,
The grouping changed, but the order of the numbers did not. Changing the order would use the commutative property, not the associative property.
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