# Finding a percentage

A percentage is a proportion that shows a number as parts per hundred. The symbol '%' means 'per cent'. 9% means 9 out of every 100, or .

Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as or . 50% can also be written as a fraction, , or a decimal, 0.5. They are all exactly the same amount.

Knowledge of converting between decimals, fractions and percentages is required.

## Calculating percentages of amounts

Percentages of amounts can be calculated by writing the percentage as a fraction or decimal and then multiplying it by the amount in question.

### Example 1

Find 16% of 40.

16% is the same as .

To find 16% of 40, multiply by 40:

(to divide by 100, bring the decimal place in by two places)

This example could also be worked out by converting the percentage to a decimal. This method may be easier to do if a calculator is available.

16% is the same as 0.16. To find 16% of 40, multiply 0.16 by 40:

.

### Example 2

Percentages of amounts can also be found using known facts about percentages. The most helpful of these facts is how to find 10% of an amount.

10% can be written as because 10% means 10 out of every 100. the fraction gives (taking out a of 10).

This means that 10% is equivalent to dividing by 10, or finding of the amount.

As finding 10% of a number means to divide by 10, you might be tempted to think that to find 20% of a number you should divide by 20. However that's not the case!

To find 10% of a number means dividing by 10 because 10 goes into 100 ten times. Therefore, to find 20% of a number, divide by 5 because 20 goes into 100 five times.

Once 10% of an amount is known, this can be manipulated to find other amounts such as 5% or 1%, or any amount that is helpful to answer the question.

Question

Find 27% of 80.

Start by finding 10% of 80 by dividing 80 by 10:

The question asks for 27%, so double 10% to get the 20% needed:

Now that 20% has been found, the remaining amount to calculate the full 27% is 7%. This can be done in lots of different ways, but one of the easiest ways is to find 1% and multiply this by 7.

1% = so 1% can be found easily by dividing the amount by 100.

1% of 80 =

So 7% = .

20% of 80 = 16 and 7% of 80 = 5.6

27% of 80 =

Find 10% of a number by dividing by 10. Find 1% of a number by dividing by 100.