How to calculate percentages

Key points

You can find the percentage of an amount mentally, by combining percentages or using . Or you may choose to use a calculator method.
To calculate , being able convert percentages to fractions, find equivalent fractions, and find fractions of an amount are useful skills.
Knowledge of the order of operations (BIDMAS) is useful in recognising that a percentage calculation can be entered into a calculator in different ways.

Find a percentage of an amount using combinations of percentages

One way to find a percentage of an amount is to use 1%, 10% and 50% as building blocks.

Write the percentage as the of two or more of 1%, 10% and 50%
Work out the percentages.
Sum the percentages to get the total percentage.

Examples

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1%, 10% and 50% can be used as building blocks for working out percentages in your head.
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A percentage can be made from a combination of percentages. For example, 60% is 50% + 10%
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1% is 1⁄100. Work out 1% by dividing by 100. This building block of 1% can be multiplied to find other percentages. For example, to find 2% multiply 1% by 2. To find 3%, multiply 1% by 3. To find 4%, multiply 1% by 4
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10% is 10⁄100 or one tenth. Work out 10% by dividing by 10. This building block of 10% can be multiplied or divided to find other percentages. For example, to find 5%, divide 10% by 2. To find 20%, multiply 10% by 2. To find 40%, multiply 10% by 4
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50% is 50⁄100 or one half. Work out 50% by dividing by 2. This building block of 50% can be used to find other percentages. For example, to find 25% divide 50% by 2. To find 75%, work out 25% and then multiply by 3. Or you could add 50% and 25%
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Find 65% of 360
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65% can be made up of 50% + 10% + 5%
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To find 65% of 360, work out 50%, 10% and 5% of 360
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Add the 50%, 10% and 5% values to find 65%. 65% of 360 is 234
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There is often more than one way to work out a percentage. 65% could be worked out as 50% + 10% + 5%. Another way could be 6 lots of 10% + 5%

Question

Given the building blocks of 50% and 10%, there is more than one way to mentally work out 45% using combinations of percentages.

Write down some ideas. Then check to see if your combinations are listed.

Find a percentage of an amount using equivalent fractions

Another method to find a percentage an amount involves equivalent fractions.

To find a percentage of an amount using equivalent fractions:

Write the percentage as a equivalent fraction.
Divide the amount by the .
Then multiply the result by the .

It is useful to know that A% of B is the same as B% of A. This is helpful to remember when calculating a trickier percentage.

Examples

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Find 30% of 160
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30% is the same as 30⁄100. This simplifies to 3⁄10. Find 30% of 160 by working out 3⁄10 of 160. This is written as 3⁄10 × 160
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Divide 160 by the denominator (10) and multiply by the numerator (3). 30% of 160 is 48
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Find 80% of 90
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80% is 80⁄100. This simplifies to 4⁄5. Find 80% of 90 by working out 4⁄5 of 90. This is written as 4⁄5 × 90
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Divide 90 by the denominator (5) and multiply by the numerator (4). 80% of 90 is 72
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Find 32% of 50
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32% of 50 is the same as 50% of 32. The percentage can be easier to work out mentally when the percentage simplifies to a fraction that is easier to work with. ½ (50%) is easier to work with than 8⁄25 (32%)
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50% of 32 is ½ of 32. This is 16
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32% of 50 is the same as 50% of 32. 32% of 50 is 16

Question

Find 75% of 24

Find a percentage of an amount using a calculator

There is more than one way to work out a percentage of an amount using a calculator:

Convert the percentage to a decimal, then find the percentage of the amount.

Divide the percentage value by 100
Multiply by the amount.

Or

Work out 1% of the amount, then find the percentage of the amount.

Divide the amount by 100
Multiply by the percentage value.

The order of operations (BIDMAS) can give further variations of the process.

Examples

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Find 73% of 680 using a calculator.
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One way to find 73% of 680 is to divide the percentage value (73) by 100. Then, multiply by the amount (680). 73 ÷ 100 x 680
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In this method the first part of the calculation converts the 73% to a decimal (0∙73). Then multiply by 680 to give 73% of 680. 73% of 680 is 496∙4
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Another way to find 73% of 680 is to work out 1% of the amount, then find the percentage of the amount.
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Divide the amount (680) by 100. Then, multiply by the percentage value (73). 680 ÷ 100 x 73
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In this method the first part of the calculation works out 1% of 680. Then, multiplying by 73 gives 73% of 680. 73% of 680 is 496∙4

Question

Use a calculator to work out 8∙2% of 3500

Practise calculating percentages

Practise calculating percentages in this quiz. You might need a pen, paper and calculator to help you.

Quiz

Real-world maths

A white waitress smiling at two customers as one of them taps their card on a card machine to pay. They have two coffee cups next to them. — Image caption,
Working out a percentage of the bill and adding a 10% tip for table service.

A customer in a restaurant may wish to give a tip when paying for a meal. They may use a mental calculation to work out a 10% or 15% payment to the person who has provided the table service. They can then leave a cash tip, or add the tip to their card payment.

Finding the percentage of an amount is useful when buying discounted goods. For example, a clothes store may offer higher discounts on particular collections within the same store. Each item may be tagged with the full price and the percentage discount. It is useful to be able to work out the price you will pay either mentally or with a calculator.

Teaching resources

Are you a teacher looking for more resources? This short video clip describes how percentage discounts can be worked out without using a calculator.

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Key points

Find a percentage of an amount using combinations of percentages

Examples

Question

Find a percentage of an amount using equivalent fractions

Examples

Question

Find a percentage of an amount using a calculator

Convert the percentage to a decimal, then find the percentage of the amount.

Work out 1% of the amount, then find the percentage of the amount.

Examples

Question

Convert the percentage to a decimal, then find the percentage of the amount.

Or

Work out 1% of the amount, then find the percentage of the amount.

Practise calculating percentages

Quiz

Real-world maths

Teaching resources

Game - Divided Islands

More on Percentages

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Key points

Find a percentage of an amount using combinations of percentages

Examples

Question

Show answerHide answer

Find a percentage of an amount using equivalent fractions

Examples

Question

Show answerHide answer

Find a percentage of an amount using a calculator

Convert the percentage to a decimal, then find the percentage of the amount.

Work out 1% of the amount, then find the percentage of the amount.

Examples

Question

Show answerHide answer

Convert the percentage to a decimal, then find the percentage of the amount.

Or

Work out 1% of the amount, then find the percentage of the amount.

Practise calculating percentages

Quiz

Real-world maths

Teaching resources

Game - Divided Islands

More on Percentages

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