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Use the associative property of multiplication

Associative property of multiplication means that changing the grouping of three whole-number factors does not change the product: (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c). 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.

Detailed Explanation: Use the associative property of multiplication

The associative property of multiplication lets you change the grouping of three factors without changing the product:

(a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c)

Use it to group factors that are easier to multiply.

Example: Find 4×25×24 \times 25 \times 2.

  1. Group the first two factors:

(4×25)×2 (4 \times 25) \times 2
  1. Multiply inside the parentheses:

100×2=200 100 \times 2 = 200
  1. Regroup the factors so the easier pair is together:

4×(25×2) 4 \times (25 \times 2)
  1. Multiply inside the parentheses first:

4×50=200 4 \times 50 = 200

Both groupings give the same product:

(4×25)×2=4×(25×2)=200(4 \times 25) \times 2 = 4 \times (25 \times 2) = 200

The grouping changed, but the order of the factors did not. The factors stayed 44, 2525, and 22 in the same order.

Learn by doing: Use the associative property of multiplication

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Multiplication - Commutative Property


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