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Use the commutative property of multiplication

Changing the order of two whole-number factors does not change the product: 3 × 4 and 4 × 3 both represent 12. In an array, this is shown by turning the arrangement so its rows and columns exchange roles, supporting multiplication-fact fluency and related division facts; the understanding is limited to whole-number multiplication with products within 100, not more general algebraic or non-whole-number cases.

Detailed Explanation: Use the commutative property of multiplication

When you multiply two whole numbers, you can switch their order without changing the answer.

For example, find 3×43 \times 4.

  1. Think of 3×43 \times 4 as 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. Turn the array. Now it 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, switching the factors gives the same product:

3×4=4×3=123 \times 4 = 4 \times 3 = 12

This can help you remember multiplication facts: if you know one fact, you also know the fact with the factors reversed.

Learn by doing: Use the commutative property of multiplication

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    Multiplication - Commutative Property

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