Calculating percentages of amounts

In a nutshell

It is often useful to calculate percentages of amounts when solving problems. Some are simple and some require a little more work.

Finding percentages of amounts

There are two methods to calculating percentages of amounts: by using simple percentages that you already know, or by converting the percentage to a fraction and multiplying.

Method 1: Using simple percentages

You can always split up a percentage into smaller simple ones. Below are some simple percentages that you need to remember how to calculate, as well as their equivalent fraction pairs.

PERCENTAGE	FRACTION	HOW TO CALCULATE
$50 \%$	$\frac{1}{2}$	Divide by two
$25\%$	$\frac{1}{4}$	Divide by four
$10\%$	$\frac{1}{10}$	Divide by ten
$5\%$	$\frac{1}{20}$	Divide by ten and then two
$1\%$	$\frac{1}{100}$	Divide by one hundred

Example 1

In a sale, everything is $17\%$ off. What saving would be made on $£200$ ?

Split $17\%$ into simple percentages.

$17\%=10\%+5\%+1\%+1\%$

Work out each of the simple percentages.

$10\%$ of $200 = 200\div10=20$

$5\%$ of $200= 10\% \div 2=20\div2=10$

$1\%$ of $200= 200\div100=2$

Add together the simple percentages.

$20+10+2+2=\underline{£32}$

Method 2: Turn into a fraction and multiply

The second method is to simply turn the percentage into a fraction and multiply by the amount. Remember that to convert from a percentage to a fraction you take the percentage as a fraction out of one hundred.

Example 2

Calculate $29\%$ of $£3300$ .

Write $29\%$ as a fraction out of one hundred.

$\frac{29}{100}$ 

Multiply by $£3300$ .

$\begin{aligned}\frac{29}{100}\times£3300=£3300 \div 100 \times 29\\=£33 \times 29 = \underline{£957} \end{aligned}$ 