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Use the associative property of multiplication

The associative property of multiplication means that when multiplying three whole numbers, changing the grouping of the factors does not change the product: (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c). This represents combining equal groups in different stages and supports efficient calculation using known facts; it does not permit changing the order of factors, which is the commutative property.

Detailed Explanation: Use the associative property of multiplication

The associative property of multiplication lets you change how three factors are grouped. The order of the factors stays the same.

For example:

(3×2)×5(3 \times 2) \times 5

First, multiply the numbers in parentheses:

3×2=63 \times 2 = 6

Then multiply by 55:

6×5=306 \times 5 = 30

Now regroup the same factors:

3×(2×5)3 \times (2 \times 5)

Multiply the numbers in parentheses first:

2×5=102 \times 5 = 10

Then multiply by 33:

3×10=303 \times 10 = 30

Both groupings give the same product:

(3×2)×5=3×(2×5)=30(3 \times 2) \times 5 = 3 \times (2 \times 5) = 30

Choose the grouping that makes a multiplication fact easier. Notice that the order stayed 33, 22, 55; only the grouping changed.

Learn by doing: Use the associative property of multiplication

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