6.2 Percentage change — Learn

Prerequisites: finding a percentage of an amount and subtracting decimals.

Objectives: calculate a percentage increase or decrease and find the percentage change.

A percentage change compares the change with the starting amount. The multiplier for a rise of $r$% is $1+r/100$. For a fall, use $1-r/100$.

Example 1. Increase £80 by 15%.

The increase multiplier is $1+15/100=1.15$.

£80 × 1.15 = £92.

Example 2. A price falls from £50 to £42. Work out the percentage decrease.

The decrease is £50 − £42 = £8.

The change as a fraction of the start is $8/50=0.16$.

So the decrease is 16%.

Watch out. Dividing by the new amount gives the wrong base. Divide the change by the starting amount. Check: £8 is 16% of £50.

Progress check

If £600 increases by 4%, what multiplier will you use? Compare it with the estimate you made in 6.1.

You should now be able to

• choose a multiplier for an increase or decrease;
• calculate the new amount;
• find percentage change by comparing the change with the starting amount.