KS3 Percentage Revision Notes
KS3 Percentage Revision Notes
Years 7, 8 and 9 | percentages.co.uk
1. Quick recap
A percentage means "out of 100". The table below shows the fraction and decimal equivalents you must know at KS3.
| Percentage | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.1 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33.3% (recurring) | 1/3 | 0.333... |
| 50% | 1/2 | 0.5 |
| 66.7% (recurring) | 2/3 | 0.667... |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.8 |
| 90% | 9/10 | 0.9 |
| 100% | 1 whole | 1.0 |
2. Finding a percentage of an amount
There are two reliable methods at KS3. Learn both.
Method a: Formula method
Amount × (percentage ÷ 100)
Worked example
Find 35% of 240.
240 × (35 ÷ 100) = 240 × 0.35 = 84
Method b: Multiplier method
A multiplier is a single decimal number that combines the percentage change into one step. This method is faster and is required for percentage increases and decreases.
Common multipliers
| Change | Multiplier |
|---|---|
| Increase by 10% | × 1.10 |
| Increase by 25% | × 1.25 |
| Decrease by 10% | × 0.90 |
| Decrease by 25% | × 0.75 |
For an increase, add the percentage to 100 and divide by 100 (e.g. 10% increase: (100 + 10) ÷ 100 = 1.10). For a decrease, subtract from 100 (e.g. 10% decrease: (100 - 10) ÷ 100 = 0.90).
3. Expressing as a percentage
(part ÷ whole) × 100
Worked example
A pupil scores 36 out of 90. What percentage is that?
(36 ÷ 90) × 100 = 0.4 × 100 = 40%
4. Percentage increase and decrease using multipliers
To increase or decrease an amount by a percentage, multiply by the appropriate multiplier.
Percentage increase
Increase 80 by 15%.
Multiplier = 1 + (15 ÷ 100) = 1.15
80 × 1.15 = 92
Percentage decrease
Decrease 120 by 20%.
Multiplier = 1 - (20 ÷ 100) = 0.80
120 × 0.80 = 96
5. Percentage change
Use this formula to find by what percentage something has increased or decreased:
Percentage change = (change ÷ original) × 100
Worked example
A price rises from £40 to £50. What is the percentage increase?
Change = £50 - £40 = £10
Percentage change = (10 ÷ 40) × 100 = 25%
The price increased by 25%.
6. Converting between fractions, decimals and percentages
You need to be able to move between all three forms. Here is a summary:
7. Practice questions
Work through all eight questions before checking your answers.
- Find 35% of 160.
- Increase £250 by 12%.
- Decrease 480 by 15%.
- A coat costs £95. In a sale, it is reduced to £76. What is the percentage decrease?
- A student scores 54 out of 72 in a test. Express this as a percentage.
- Write 45% as a fraction in its simplest form.
- Write 7/20 as a percentage.
- A salary rises from £28,000 to £31,500. What is the percentage increase? Give your answer to 1 decimal place.