Percentages

Without a calculator, build the percentage from easy ones: 10% is ÷ 10, 1% is ÷ 100, and 50% is ÷ 2.

With a calculator, multiply by the percentage as a decimal: 35% is 0.35.

Example: without a calculator, find 35% of £80.

1. 10% = £8, so 30% = £24
2. 5% = half of 10% = £4
3. 35% = £24 + £4 = £28

Example: with a calculator, find 17.5% of £64.

1. 17.5% = 0.175
2. 0.175 × 64 = £11.20

1. Write the two amounts in the same units.
2. Divide the part by the whole.
3. Multiply by 100.

Example: Sam scores 18 out of 24. What percentage is this?

1. 18 ÷ 24 = 0.75
2. 0.75 × 100 = 75%

Example: write 45p as a percentage of £3.

1. Same units: £3 = 300p
2. 45 ÷ 300 = 0.15
3. 15%

A multiplier does the increase or decrease in one step.

• Increase by 15%: 100% + 15% = 115%, so multiply by 1.15.
• Decrease by 15%: 100% − 15% = 85%, so multiply by 0.85.

Example: increase £240 by 15%.

1. Multiplier: 1.15
2. 240 × 1.15 = £276

Example: decrease £240 by 30%.

1. Multiplier: 1 − 0.30 = 0.7
2. 240 × 0.7 = £168

Percentage change = change ÷ original amount × 100 (learn this)

1. Work out the change (new − original).
2. Divide by the original amount.
3. Multiply by 100.

Example: a price rises from £50 to £62. Find the percentage increase.

1. Change: 62 − 50 = £12
2. 12 ÷ 50 = 0.24
3. 24% increase

Example: a population falls from 80 to 68. Find the percentage decrease.

1. Change: 80 − 68 = 12
2. 12 ÷ 80 = 0.15
3. 15% decrease