Percentage of an Amount

Per cent means out of 100. So 15\% means 15 out of every 100, and 15\%=\frac{15}{100}. The whole amount is always 100\%.

In the exam, the first questions ask you to work out a percentage of a number, such as 30\% of 90, for 1 or 2 marks. Later questions put a percentage into a story, such as a deposit, the rest of a bill or two amounts to compare, for 3 or 4 marks.

Paper 1 has no calculator, so learn the methods on this page that use easy steps. On Papers 2 and 3 you may use a calculator, but you still need to write down the calculation you do.

Some percentages are simple fractions. Learn what each one tells you to do to the whole amount.

• 50\% is one half, so divide by 2
• 25\% is one quarter, so divide by 4
• 75\% is three quarters, so divide by 4, then multiply by 3
• 10\% is one tenth, so divide by 10
• 20\% is one fifth, so divide by 5
• 1\% is one hundredth, so divide by 100

For example, with £60: 50\% is £30, 25\% is £15, 75\% is £45, 10\% is £6, 20\% is £12 and 1\% is £0.60. A percentage over 100\% is more than the whole, so 125\% is \pounds 60+\pounds 15=\pounds 75

To find 10\%, divide by 10. This splits the whole into ten equal parts, and one part is 10\%.

From 10\% you can build other percentages. 20\% is two lots of 10\%, 30\% is three lots, and 5\% is half of 10\%. So 15\%=10\%+5\% and 35\%=30\%+5\%.

For a percentage such as 12\%, use 1\% as well. 1\% of 420 is 420\div100=4.2, so 2\% is 8.4 and 12\% is 42+8.4=50.4. Write every step down like this. Examiners can only give method marks for steps they can see.

Any percentage can be written as a decimal by dividing by 100. So 38\%=0.38 and 5\%=0.05. This decimal is called the multiplier.

To find a percentage of an amount, multiply the amount by the multiplier.

\frac{\text{percentage}}{100}\times\text{amount}

This works for any percentage, even an awkward one such as 56\% or 17.5\%.

Write the calculation in your working, such as 0.38\times1250. Writing only "38\% of 1250" does not show a method, so it earns no marks if the answer is wrong.

Many questions use a percentage and then ask about the rest. The rest is 100\% take away the percentage used. If 70\% of the 60 seats on a bus are taken, the other 30\% are empty.

You can find the part used and subtract it: 70\% of 60 is 42, and 60-42=18 empty seats. Or find the rest straight away: 30\% of 60 is 18. Both ways give the same answer.

Read carefully when a second percentage appears. A percentage "of what is left" is a percentage of the remainder, not of the starting amount. Work out what is left first: that is the new whole.

Sometimes you are told a part and its percentage, and asked for the whole. For example, 30\% of the pupils in a club is 27 pupils. The 27 is only 30\%, not 100\%.

Find 10\% first: 27\div3=9. Then 100\% is 10\times9=90 pupils. The whole must be bigger than the part you were given.

• Getting the zeros wrong when finding 10%. Dividing by 10 takes off one zero: 10\% of 36\,000 is 3600.
• Halving 10\% to get 20\%. 20\% is two lots of 10\%, so double it: 10\% of 360 is 36, so 20\% is 72.
• Writing "38\% of 1250" as the working. Write a calculation, such as 0.38\times1250 or \frac{38}{100}\times1250.
• Stopping one step too soon. If the question asks what is left or what someone else pays, subtract the part you found.
• Taking the second percentage of the starting amount. A percentage "of what is left" uses the amount that is left.
• Treating the part you are given as 100\%. If £72 is 60\%, find 10\% first, then multiply by 10.