Percentages

There’s a few things you might be asked to do with percentages….

Find X% of Y

Just turn the percentage into a decimal then multiply.

So 30% of £80 = 0.3 x £80 = £24

What Is The Amount After An X% Increase / Decrease?

E.g. A car’s price is reduced by 45%. It originally cost £80. What does it cost now?

Write 45% as a decimal and multiply by £80 to find the change in price.

0.45 x £80 = £36.

Therefore you know it was reduced by 36 quid. So the new cost is:

£80 – £36 = £44

Express X As A Percentage Of Y

E.g. Express 76p as a percentage of £2.34.

Make sure the figures are in the same units – so here put them both in pence.

Then just divide 76p by 234p and multiply by 100:

(76/234) x 100 = 32.48%

Find The Percentage Changepercentage-change-formulaSo if you buy an apple (a classic maths problem situation) for 20p and sell it for 30p your percentage profit is:


(30-20)/20 x 100 = 50%

Finding The Original Value

These can be tricky to recognise…but if you have to work out the original amount then don’t panic and follow this method:

  • write the new amount as a percentage of the original
  • divide by whatever this percentage is to find 1% of the original
  • Multiply by 100 to get the original

So if a car goes up in price by 20% and is now £7,200 to find the original amount you have to:

  • Realise that £7,200 is 120% of the original
  • Divide £7,200 by 120 to get 1% of the original
  • Multiply by 100

So original price = (£7,200/120) x 100 = £6000