Percentages of amounts
- Per cent means 'out of 100'.
- Without a calculator: 10% = divide by 10, 1% = divide by 100, then build up (e.g. 35% = 10% + 10% + 10% + 5%).
- With a calculator, use a multiplier: 35% of 80 = 0.35 × 80 = 28.
One number as a percentage of another
- Divide, then multiply by 100.
- 18 out of 24 = 18 ÷ 24 × 100 = 75%.
Percentage increase and decrease
- Increase by 15%: multiply by 1.15. Decrease by 15%: multiply by 0.85.
- Percentage change = change ÷ original × 100.
Reverse percentages
- Divide by the multiplier to find the original amount.
- After a 20% increase a price is £96, so the original price is £96 ÷ 1.2 = £80.
- Don't take 20% off the new amount: that gives the wrong answer.
Interest and depreciation
- Simple interest adds the same amount every year.
- Compound interest uses the multiplier to a power: £500 at 3% for 4 years = 500 × 1.03⁴.
- Depreciation (losing value) uses a multiplier less than 1, e.g. 10% a year = × 0.9 each year.
Key terms
- Percentage
- A number out of 100.
- Multiplier
- The decimal you multiply by to find or change a percentage, e.g. 1.15 for a 15% increase.
- Percentage change
- Change ÷ original × 100.
- Reverse percentage
- Finding the original amount by dividing by the multiplier.
- Simple interest
- Interest that is the same amount every year.
- Compound interest
- Interest added to the total each year, so it grows by the same percentage each time.
- Depreciation
- A decrease in value over time.