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Use the commutative property of multiplication

Multiplication of whole numbers gives the same product when the order of the factors is reversed: a×b=b×aa \times b = b \times a. An array or area model shows this by rotating the same rows and columns, helping connect related multiplication facts and avoid treating reversed factors as different products; this property changes order, not grouping or the factors themselves.

Detailed Explanation: Use the commutative property of multiplication

The commutative property of multiplication means you can switch the order of the factors without changing the product:

a×b=b×aa \times b=b \times a

For example, find the product of 3×43 \times 4.

  1. Think of 3×43 \times 4 as an array with 3 rows of 4:

∙∙∙∙∙∙∙∙∙∙∙∙\begin{array}{cccc} \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet \end{array}

  1. Count the objects. There are 1212, so:

3×4=123 \times 4=12

  1. Rotate the array. It now has 4 rows of 3:

∙∙∙∙∙∙∙∙∙∙∙∙\begin{array}{ccc} \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet \end{array}

  1. The number of objects is still 1212, so:

4×3=124 \times 3=12

Therefore:

3×4=4×3=123 \times 4=4 \times 3=12

The commutative property changes the order of the factors, not the factors themselves.

Learn by doing: Use the commutative property of multiplication

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    Multiplication - Commutative Property

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