# 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 *$7$.