Associative property of multiplication means that changing the grouping of three whole-number factors does not change the product: . This supports choosing convenient partial products and interpreting equal groupings in arrays or area models, while distinguishing regrouping from changing factor order; the focus is on whole-number computation, not formal proof or generalized algebraic treatment.
The associative property of multiplication lets you change the grouping of three factors without changing the product:
Use it to group factors that are easier to multiply.
Example: Find .
Group the first two factors:
Multiply inside the parentheses:
Regroup the factors so the easier pair is together:
Multiply inside the parentheses first:
Both groupings give the same product:
The grouping changed, but the order of the factors did not. The factors stayed , , and in the same order.
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