Notes
Key idea: "per cent" means "out of 100". 1% is one hundredth. 50% is 50 out of 100, which is a half.
Facts to know by heart
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 10% | 1/10 | 0.1 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |
| 100% | 1 | 1 |
Finding a percentage of an amount
Build it from the easy ones. Find 10% by dividing by 10, and 1% by dividing by 100. Then add or halve.
Example: find 15% of 40.
- 10% of 40 = 4
- 5% of 40 = 2 (half of 10%)
- 15% = 4 + 2 = 6
Example: find 35% of 60.
- 10% of 60 = 6, so 30% = 18
- 5% of 60 = 3
- 35% = 18 + 3 = 21
Handy trick: a% of b is always the same as b% of a. So 4% of 50 is the same as 50% of 4, which is 2. Swap them round if one version is easier.
Turning fractions and decimals into percentages
- Fraction to percentage: make the denominator 100. 7/20 = 35/100 = 35%.
- If you can't, divide the top by the bottom and multiply by 100.
- Decimal to percentage: multiply by 100. 0.35 = 35%.
One number as a percentage of another
Write it as a fraction, then convert. 18 out of 24 is 18/24 = 3/4 = 75%.
Increasing and decreasing
Find the percentage of the amount, then add it (increase) or subtract it (decrease).
Example: a £60 jumper goes up in price by 10%. 10% of £60 = £6, so the new price is £60 + £6 = £66.
Common mistakes
- Thinking 50% of a number means dividing 50 by the number. It means half of the number.
- Forgetting to subtract (or add) after finding the percentage in a sale question. The percentage is the change, not the new price.
- Dividing by the wrong number: 10% is dividing by 10, but 20% is not dividing by 20. Find 10% and double it.
Websink Prep UK · 11+ Maths: Percentages
Name: ____________________ Date: ____________ Score: ______
- Work out.
- (a) 10% of 70
- (b) 25% of 80
- (c) 5% of 60
- (d) 15% of 40
- (e) 75% of 120
- (f) 20% of 35
- Write each as a percentage.
- (a) 3/5
- (b) 0.35
- (c) 7/20
- A shirt costs £24. It is reduced by 25%. What is the sale price?
- In a test, Maya got 18 out of 24 questions right. What percentage did she get right?
- A jumper costs £60. The price goes up by 10%. What is the new price?
- Which is bigger, 40% of 50 or 30% of 70? Show your working.
- There are 30 children in a class. 60% are girls. How many boys are there?
- Ali got 17 out of 20 on a spelling test. What is that as a percentage?
- 35% of a number is 14. What is the number?
- Challenge: a coat costs £80. In a sale it is reduced by 30%. Then an extra 10% is taken off the sale price. What does it cost now?
Answers and working
- Use 10% and 1% as building blocks.
- (a) 7
- (b) 20
- (c) 10% = 6, so 5% = 3
- (d) 10% = 4, 5% = 2, so 15% = 6
- (e) 75% is three quarters: 120 ÷ 4 = 30, then 30 × 3 = 90
- (f) 10% = 3.5, so 20% = 7
- Convert.
- (a) 3/5 = 60/100 = 60%
- (b) 0.35 × 100 = 35%
- (c) 7/20 = 35/100 = 35%
- 25% of £24 = £6, and £24 − £6 = £18.
- 18/24 = 3/4 = 75%.
- 10% of £60 = £6, and £60 + £6 = £66.
- 40% of 50 = 20. 30% of 70 = 21. So 30% of 70 is bigger.
- 60% of 30 = 18 girls. Boys = 30 − 18 = 12.
- 17/20 = 85/100 = 85%.
- 35% = 14, so 5% = 2 (since 14 ÷ 7 = 2). 100% is 20 times 5%, so 2 × 20 = 40.
- 30% of £80 = £24, so the sale price is £56. 10% of £56 = £5.60, so the final price is £56 − £5.60 = £50.40.
Quick quiz
Practise with real exam questions
Real 11+ papers are set by GL Assessment, CEM or the school itself and are mostly not published, so practice here uses original exam-style questions.