What is the commutative property?

The commutative property means that the order in which numbers are multiplied has no effect on the answer.

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Chapter overview

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Maths

Mental maths strategies

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Summary

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Mental maths strategies

In a nutshell

Mental calculations can be performed faster by reorganising calculations into an easier format.

Commutative property

The commutative property means that the order in which you multiply or add numbers will have no effect on the answer.

Example 1

Demonstrate the commutative law with $4 \times 3$ .

Calculate $4 \times 3$ .

$4\times 3 = 12$

Reorder the numbers to $3 \times4$ .

$3 \times 4 =\underline{12}$

Note: The commutative property can be applied even if there are more than two numbers being multiplied together.

Factor pairs

Factor pairs are two whole numbers which multiply to give the original number. Factor pairs can be used to break up a multiplication into easier steps.

Example 2

How many factor pairs does $12$ have?

Find all the whole numbers which multiply to give $12$ .

${\begin{aligned} {12 \times1 = 12} \\ {6 \times 2=12}\\ {4 \times 3=12} \end{aligned}}$

There are $\underline{3}$ factor pairs for $12$ .

Note: The commutative property means the factor pairs can be written in the opposite order.

Example 3

Calculate $7 \times 16$ .

$16$ can be split into $8$ and $2$ . Use this to work out $7 \times 16$ .

$7 \times 8 \times 2$

Multiply the numbers in an order you find easy.

$\begin{aligned} 7\times 8 &= 56 \\ 56 \times 2 &= 112 \\ \\ &or \\ \\ 7 \times 2 &= 14 \\ 14 \times 8 &= 112 \end{aligned}$ 

Therefore, $7 \times 16 = \underline{112}$ 

Note: $7$ is a prime number which means its only factor pair is $1$ and $7$ .

Mental maths strategies

In a nutshell

Mental calculations can be performed faster by reorganising calculations into an easier format.

Commutative property

The commutative property means that the order in which you multiply or add numbers will have no effect on the answer.

Example 1

Demonstrate the commutative law with $4 \times 3$ .

Calculate $4 \times 3$ .

$4\times 3 = 12$

Reorder the numbers to $3 \times4$ .

$3 \times 4 =\underline{12}$

Note: The commutative property can be applied even if there are more than two numbers being multiplied together.

Factor pairs

Factor pairs are two whole numbers which multiply to give the original number. Factor pairs can be used to break up a multiplication into easier steps.

Example 2

How many factor pairs does $12$ have?

Find all the whole numbers which multiply to give $12$ .

${\begin{aligned} {12 \times1 = 12} \\ {6 \times 2=12}\\ {4 \times 3=12} \end{aligned}}$

There are $\underline{3}$ factor pairs for $12$ .

Note: The commutative property means the factor pairs can be written in the opposite order.

Example 3

Calculate $7 \times 16$ .

$16$ can be split into $8$ and $2$ . Use this to work out $7 \times 16$ .

$7 \times 8 \times 2$

Multiply the numbers in an order you find easy.

$\begin{aligned} 7\times 8 &= 56 \\ 56 \times 2 &= 112 \\ \\ &or \\ \\ 7 \times 2 &= 14 \\ 14 \times 8 &= 112 \end{aligned}$ 

Therefore, $7 \times 16 = \underline{112}$ 

Note: $7$ is a prime number which means its only factor pair is $1$ and $7$ .

Frequently Asked Questions (FAQ)

FAQs

Question: What are factor pairs?

Answer: Factor pairs are two whole numbers which multiply to give the original number.
Question: What is the commutative property?

Answer: The commutative property means that the order in which numbers are multiplied has no effect on the answer.

Theory

Exercises

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Mental maths strategies

Mental maths strategies

In a nutshell

Commutative property

Example 1

Factor pairs

Example 2

Example 3

Mental maths strategies

In a nutshell

Commutative property

Example 1

Factor pairs

Example 2

Example 3

Now you’ve read the summary, have a go at the exercises!