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Chapter Overview

Maths

Number and place value

Addition and subtraction

Multiplication and division

Fractions

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Geometry - properties of shapes

Geometry - position and direction

Statistics

Ratio and proportion

Algebra

Maths

Calculating percentages of amounts

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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%50 \%​​

​12\frac{1}{2}​​

Divide by two

​25%25\%​​

​14\frac{1}{4}​​

Divide by four

​10%10\%​​

​110\frac{1}{10}​​

Divide by ten

​5%5\%​​

​120\frac{1}{20}​​

Divide by ten and then two

​1%1\%​​

​1100\frac{1}{100}​​

Divide by one hundred



Example 1

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


Split 17%17\% into simple percentages.

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


Work out each of the simple percentages.

10%10\%  of 200=200÷10=20200 = 200\div10=20

5%5\%  of 200=10%÷2=20÷2=10200= 10\% \div 2=20\div2=10

1%1\%  of 200=200÷100=2200= 200\div100=2

​​​

Add together the simple percentages.

20+10+2+2=£32‾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%29\% of £3300£3300.


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

29100\frac{29}{100}​​


Multiply by £3300£3300.

29100×£3300=£3300÷100×29=£33×29=£957‾\begin{aligned}\frac{29}{100}\times£3300=£3300 \div 100 \times 29\\=£33 \times 29 = \underline{£957} \end{aligned}​

Want to find out more? Check out these other lessons!

Mean, median, mode and range

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Frequently Asked Questions (FAQ)

FAQs

  • Question: How do I work out a percentage using fractions?

    Answer: Turn the percentage into a fraction and multiply by the amount. To convert from a percentage to a fraction you take the percentage as a fraction out of one hundred.

  • Question: How do I work out 1% of a number?

    Answer: To work out 1% of a number, divide by one hundred.

  • Question: How do I work out 10% of a number?

    Answer: To work out 10% of a number, divide by ten.

  • Question: How do I work out 50% of a number?

    Answer: To work out 50% of a number, divide by two.

  • Question: How do I find a percentage of an amount?

    Answer: 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.

Theory

Exercises

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