Percentage Change

Explore increase, decrease, reverse percentages and repeated compound growth or decay using multipliers.

Curriculum rangeYears 7–11

Amount

200

Increasing by 20% means the new amount is 120% of the original -- as a multiplier, that's 1.2.

200 × 1.2 = 240

Learning notes

Percentage Change essentials

Keep these rules beside you while you explore and practise.

\text{Increase multiplier}=1+\dfrac r{100}

\text{Decrease multiplier}=1-\dfrac r{100}

\%\text{ change}=\dfrac{\text{change}}{\text{original}}\times100

If a final amount equals m times the original, divide by m to recover the original.

\text{Original}=\dfrac{\text{final}}{m}

A=P\left(1\pm\dfrac r{100}\right)^n

The percentage acts on the new amount each time.

💡Important: a 20% increase followed by a 20% decrease does not return to the starting amount.