Percentage Change
Year 8 🔢 Number Percentage increase/decrease, reverse percentages, compound interest.
📈 Percentage Increase and Decrease
Percentage change measures how much a quantity has grown or shrunk relative to its original value.
⚡ Key Formula
$$\% \text{ change} = \frac{\text{change}}{\text{original}} \times 100$$Example: Price rises from £40 to £52. Change = £12. $\% \text{ increase} = \frac{12}{40} \times 100 = 30\%$
✖️ The Multiplier Method
The multiplier method is the most efficient way to apply a percentage change in one step.
⚡ Multipliers
Increase by $r\%$: multiply by $\left(1 + \frac{r}{100}\right)$Decrease by $r\%$: multiply by $\left(1 - \frac{r}{100}\right)$
Example: Increase £350 by 20%: $350 \times 1.20 = £420$
Example: Decrease 80 kg by 15%: $80 \times 0.85 = 68$ kg
🔄 Reverse Percentage
Find the original value before a percentage change was applied.
- Identify the multiplier that was used.
- Divide the current value by that multiplier.
Example: After a 25% increase, a price is £75. Original $= \frac{75}{1.25} = £60$
Never subtract a percentage from the new value — always divide by the multiplier to reverse the change.
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Percentage Change
🎬
Interactive demonstration available in the Calculator tab!
📈 Percentage Change Tool
🧮
Use the interactive inputs above to explore this topic!
Calculator tools are loading for all Cambridge topics.