## 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 %.

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

10% = 10/100

50% = 50/100

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

100% = 100/100

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

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

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

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

Work out the cost of the tax."

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

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

£95 × 20 ÷ 100 = £19

A good rule to remember is,

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

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

For example,

50 ÷ 100 = 0.5, so 1% of 50 is 0.5

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

2% of 50 is 1 (0.5 × 2 = 1)

10% of 50 is 5 (0.5 × 10 = 5)

40% of 50 is 20 (0.5 × 40 = 20)

75% of 50 is 37.5 (0.5 × 75 = 37.5)

6.8% of 50 is 3.4 (0.5 × 6.8 = 3.4)

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