Substituting numbers into an expression

In a nutshell

Substitution means replacing the variable with a number. Substitution helps find the value of simple expressions and formulae. You should be able to substitute positive or negative numbers. Take care when substituting in for more than one variable or with powers.

Recap on negative numbers

+ \times + = +

+ \times - = -

- \times + = -

- \times - = +

Substitution

Substitute the value into the expression and then calculate the answer.

Example 1

Find the value of $6n+7$ when $n=8$ .

$\begin {aligned}6n+7 &= 6 \times 8 + 7 \\ &=\underline {55} \\\end {aligned}$

Example 2

Find the value of $6n+7$ when $n=-2$ .

$\begin {aligned}6n+7 &= 6 \times -2 + 7 \\ &= \underline{-5} \\\end {aligned}$

Example 3

Find the value of $\frac {ab} c$ when $a=15, b=4, c=3$ .

$\begin {aligned}\frac {ab} c &= \frac {15 \times 4} 3 \\ &= \underline{20} \\\end {aligned}$

Example 4

Maths; Formulae and equations; KS3 Year 7; Substituting numbers into an expression

The volume of the cuboid is given by $V = Lwh$ . Find the volume when $L=5, w=2, h=3$ .

$\begin {aligned}V &= L \times w \times h \\& = 5 \times 2 \times 3 \\&= \underline{30} \end {aligned}$