3.4 Calculating fractions and percentages of numbers

Finally, let’s consider how you would work out what , or 75%, of 36 is.

First think about what of 36 means. It means divide 36 into 4 equal parts or quarters .

Then, since we want three-quarters, which is three times as big, we multiply one of these parts by three .

So of 36 is 27.

We can write this calculation as , which means the same thing as , or

So ‘ of’ a number means multiply that number by

Working out 75% of a number can be done in a similar way if you remember that So 75% of 40 is:

Some calculators will convert directly between fractions and percentages and find the percentage of a number at the press of a button. However, it is worth making sure that you understand the meaning of fractions and percentages before letting your calculator do the work for you. This will enable you to check that the answer you obtain is reasonable, for example, 48% of a quantity should be just less than half of it.

In summary, you can see that fractions, ratios and percentages are all ways of expressing a proportion. So, for example, if you eat of a pie, the ratio of the amount you eat to the total pie is 1 : 4, and the percentage that you eat is 25%.