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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 \(\frac{9}{100}\).

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, \(\frac{1}{2}\), or a decimal, 0.5. They are all exactly the same amount.

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 \(\frac{16}{100}\).

To find 16% of 40, multiply \(\frac{16}{100}\) by 40:

\(\frac{16}{100} \times 40\)

\(= \frac{16}{100} \times\frac{40}{1}\)

\(= \frac{16 \times 40}{100 \times 1}\)

\(= \frac{640}{100} = 6.4\) (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:

\(0.16 \times 40 = 6.4\).

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 \(\frac{10}{100}\) because 10% means 10 out of every 100. the fraction \(\frac{10}{100}\) gives \(\frac{1}{10}\) (taking out a of 10).

This means that 10% is equivalent to dividing by 10, or finding \(\frac{1}{10}\) 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.