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.

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 $$200= 200\div100=2$$

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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 $$£3300$$.

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