To find a percentage of an amount without a calculator, build it up from easy parts: 10% is a tenth, 5% is half of 10%, and 1% is a hundredth. To increase or decrease by a percentage, either work out the change and add or subtract it, or multiply by a decimal multiplier such as 1.12 for a 12% increase. To write one number as a percentage of another, divide and multiply by 100.
Percentage methods
- 10% = ÷ 10, 1% = ÷ 100, 50% = ÷ 2, 25% = ÷ 4
- Increase by p%: multiply by 1 + p/100 (12% increase: × 1.12)
- Decrease by p%: multiply by 1 − p/100 (15% decrease: × 0.85)
- One number as a percentage of another: (part ÷ whole) × 100
Finding a percentage of an amount
Without a calculator, split the percentage into easy pieces. 10% means divide by 10, 5% is half of that, and 1% means divide by 100. For 15% of 260: 10% is 26, 5% is 13, so 15% is 39. With a calculator, write the percentage as a decimal and multiply: 17.5% of 64 is 0.175 × 64.
Percentage increase and decrease
One method is to find the percentage and then add it on or take it off. The quicker method uses a multiplier: a 12% increase means you end with 112% of the original, so multiply by 1.12. A 15% decrease leaves 85%, so multiply by 0.85. Multipliers are especially useful for repeated changes, such as compound interest.
Writing one number as a percentage of another
Divide the part by the whole, then multiply by 100. The whole is the total you are comparing with, so read the question carefully: if 18 of 40 students walk to school, the percentage who walk is 18 ÷ 40 × 100 = 45%.
VAT, discounts and profit
Real contexts use the same methods. Adding 20% VAT to a price multiplies it by 1.2; a 30% discount multiplies it by 0.7. If a question asks how much is taken off, give the discount itself; if it asks for the sale price, give the amount left.
Checking your answer
An increase should give a bigger number and a decrease a smaller one. Estimates help too: 15% of 260 should be a little less than a fifth of 260, which is 52.
Worked examples
Example 1. Work out 15% of 260 without a calculator.
- 10% of 260 = 26.
- 5% = half of 26 = 13.
- 15% = 26 + 13.
Answer: 39.
Example 2. Decrease 200 by 15%.
- 15% of 200 = 30.
- 200 − 30. (Or multiply by 0.85.)
Answer: 170.
Example 3. Increase £85 by 12%.
- The multiplier for a 12% increase is 1.12.
- 85 × 1.12.
Answer: £95.20.
Example 4. Work out 17.5% of 64.
- 17.5% = 0.175.
- 0.175 × 64.
Answer: 11.2.
Example 5. 18 out of 40 students walk to school. What percentage walk?
- 18 ÷ 40 = 0.45.
- 0.45 × 100.
Answer: 45%.
Example 6. A laptop costs £240 before VAT. VAT of 20% is added. Work out the price including VAT.
- Multiplier for a 20% increase: 1.2.
- 240 × 1.2.
Answer: £288.
Common mistakes
- Using the wrong whole. When writing one number as a percentage of another, divide by the total being compared with.
- Using 0.15 as a decrease multiplier. A 15% decrease uses × 0.85, not × 0.15.
- Giving the change instead of the new amount. Check whether the question asks for the increase or the new total.
- Writing 1.2 for a 2% increase. A 2% increase is × 1.02.
- Money answers with one decimal place. £95.2 should be written as £95.20.
How percentages are examined
Percentages appear on every paper of Edexcel GCSE (1MA1) and Edexcel International GCSE (4MA1), at Foundation and Higher tier, on both calculator and non-calculator papers. Common question types:
- find a percentage of an amount without a calculator
- increase or decrease an amount by a percentage
- write one number as a percentage of another
- solve a VAT, discount or best-buy problem
The percentages worksheet has questions and full answers, and the GCSE number revision engine gives unlimited practice.
Next, see percentage change and reverse percentages. Repeated percentage change is covered in compound interest.
Frequently asked questions
How do you find a percentage of an amount?
Without a calculator, build it from 10%, 5% and 1%. With a calculator, write the percentage as a decimal and multiply.
What is the multiplier for a 15% decrease?
0.85, because 100% − 15% = 85%.
How do you write one number as a percentage of another?
Divide the first number by the second, then multiply by 100.