How to find a percentage of an amount using bar models

Key points

can be useful when finding a an amount.
To find a of an amount, you need to be able to divide 100% into equal values. For example, divide 100% into 10 lots of 10%, 5 lots of 20%, 4 lots of 25% etc.
Understanding multiplication as well as division can be important when finding a percentage of an amount.

To find a percentage of an amount using a :

Draw a bar to represent 100%, the whole amount.
Split the bar into equal percentage parts. The parts need to be a of 100% and a factor of the percentage to be worked out. This is because you will need to combine some of these parts to make the required percentage.
Divide the whole amount by the number of parts in the bar. This gives the value of one percentage part.
Multiply the value of one part by the number of parts needed to make the percentage.

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Find 40% of 820
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820 is 100%
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Split the bar into 10 equal percentage parts. 40% is 4 lots of 10%. 10 is a factor of 100 and also of 40. Split the bar into 10% parts.
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Divide the whole amount (820) by the number of parts in the bar (10). 10% of 820 is 82
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40% is 4 lots of 10%. Multiply the value of one part (82) by the number of parts needed to make the percentage (4). 40% of 820 is 328
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Find 75% of 480
Image caption,
480 is 100%
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Split the bar into 4 equal percentage parts. 75% is 3 lots of 25%. 25 is a factor of 100 and also of 75. Split the bar into 25% parts.
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Divide the whole amount (480) by the number of parts in the bar (4). 25% of 480 is 120
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75% is 3 lots of 25%. Multiply the value of one part (120) by the number of parts needed to make the percentage (3). 75% of 480 is 360

A 100% bar split into a number of parts that is not a factor of 100 will give percentages that are .

Bar models can still be used to find the percentage of an amount.

For example:

33 1⁄3% is 1⁄3
A 100% bar split into 3 equal parts of 33 1⁄3% can be used to work out
33 1⁄3 % and 66 2⁄3%.
12 1⁄2% is 1⁄8
A 100% bar split into 8 equal parts of 12 1⁄2% can be used to work out
12 1⁄2%, 37 1⁄2% etc

Image caption,
Work out 37 1⁄2% of 600
Image caption,
600 is 100%
Image caption,
Split the bar into 8 equal parts of 12 1⁄2%. 37 1⁄2% is 3 lots of 12 1⁄2%
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Divide the whole amount (600) by the number of parts in the bar (8). 12 1⁄2% of 600 is 75
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37 1⁄2% is 3 lots of 12 1⁄2%. Multiply the value of one part (75) by the number of parts needed to make the percentage (3). 37 1⁄2% of 600 is 225
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Work out 33 1⁄3% of 555
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555 is 100%
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Split the bar into 3 equal parts of 33 1⁄3%. 33 1⁄3% is one part.
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Divide the whole amount (555) by the number of parts in the bar (3). This gives the value of one part. No multiplication is needed as only 33 1⁄3% is required. 33 1⁄3% of 555 is 185