## Award in Mathematics -

## Number and Measure (Level 1)

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## Topic 14: Calculating percentages

A percentage is a fraction that always has a denominator (bottom number) of 100. The symbol for 'percent' is %.

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1% = 1/100 (1 equal part out of 100)

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10% = 10/100

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50% = 50/100

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99% = 99/100 (99 out of 100)

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100% = 100/100

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A good way to visualise percentages is to think of the battery level indicator for a mobile phone or tablet.

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You will sometimes be asked to calculate a certain percentage of a given amount.

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A good example is the amount of tax that must be paid on a bill. Here is an example.

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"An electric bill was £95 plus tax at 20%

Work out the cost of the tax."

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Remember that a percentage is like a fraction 'out of 100'. So 20% = 20/100.

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So you can work out 20% of £95 like this:

£95 × 20 ÷ 100 = £19

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A good rule to remember is,

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"If you work out 1% of a number you can work out ANY percentage of it."

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This means doing the '÷ 100' part of the calculation first, to find 1%.

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For example,

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50 ÷ 100 = 0.5, so 1% of 50 is 0.5

Now it is easy (with a calculator) to find any percentage of 50:

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2% of 50 is 1 (0.5 × 2 = 1)

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10% of 50 is 5 (0.5 × 10 = 5)

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40% of 50 is 20 (0.5 × 40 = 20)

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75% of 50 is 37.5 (0.5 × 75 = 37.5)

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6.8% of 50 is 3.4 (0.5 × 6.8 = 3.4)

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99.9% of 50 is 49.95 (0.5 × 99.9 = 49.95)

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