Percentages turn up everywhere: discounts, tips, exam marks, interest rates, test scores. Most of them can be worked out in your head in a few seconds once you know a handful of building blocks. This guide shows those building blocks, then uses them for the questions people actually ask: what is 15% of this, what percentage is that, and what was the price before the discount?
Per cent means "per hundred". So 25% is 25 out of every 100, which is the fraction 25/100 or the decimal 0.25. Finding 25% of a number means multiplying by 0.25, or taking a quarter of it.
That link between percentages, fractions and decimals is the whole trick. Every method below swaps a hard-looking percentage for an easy fraction or a few easy steps.
To find 10% of a number, divide it by 10. To find 1%, divide it by 100. Both mean moving the digits one or two places.
Almost any percentage can be built from these. 5% is half of 10%, 20% is double 10%, and 2% is double 1%.
For big percentages, it is often faster to work out what is left. 70% is 100% minus 30%, and 30% of 250 is 75, so 250 − 75 = 175. Same answer, which is a good check.
Some percentages are simple fractions in disguise. These are worth knowing by heart:
| Percentage | Fraction | To find it |
|---|---|---|
| 50% | 1/2 | halve |
| 25% | 1/4 | halve, then halve again |
| 75% | 3/4 | find a quarter, then times 3 |
| 20% | 1/5 | divide by 5 |
| 12.5% | 1/8 | halve three times |
| 33⅓% | 1/3 | divide by 3 |
So 20% of 80 is 80 ÷ 5 = 16. For 75% of 48, a quarter is 48 ÷ 4 = 12 and three quarters is 12 × 3 = 36. For 12.5% of 64, halve three times: 32, 16, 8. Our fraction to percentage table lists many more of these pairs.
A percentage of a number is the same as that number's percentage of the first one: 8% of 50 is the same as 50% of 8. Half of 8 is 4, so 8% of 50 is 4. In the same way, 4% of 75 is 75% of 4, which is 3.
It works because both mean the same multiplication: 8 × 50 ÷ 100. Use it whenever one way round is much easier than the other.
Write it as a fraction, simplify, then turn the fraction into a percentage.
If the fraction doesn't simplify nicely, divide to get a decimal and multiply by 100. Our guide to quick division techniques helps with that step.
Here the percentage is known and the whole is missing. Work from the part you know to 1% or 10%, then up to 100%.
30 is 15% of a number. What is the number? If 15% is 30, then 5% is a third of that, 10. And 100% is twenty lots of 5%, so the number is 20 × 10 = 200. Check: 10% of 200 is 20 and 5% is 10, so 15% is 30. Correct.
A coat costs 64 after a 20% discount. What was the full price? The sale price is 80% of the original. If 80% is 64, then 10% is 64 ÷ 8 = 8, and 100% is 80. So the coat cost 80 before the discount.
A common mistake is to add 20% of the sale price back on. That gives 76.80, which is wrong, because the discount was 20% of the original price, not 20% of the sale price.
To increase 60 by 15%, find 15% (that is 9) and add it on: 60 + 9 = 69. To decrease 240 by 35%, find 35% of 240, which is 84, and take it off: 240 − 84 = 156.
A faster way for a calculator, or for repeated changes, is the multiplier. A 35% decrease leaves 65%, so multiply by 0.65: 240 × 0.65 = 156. A 15% increase means multiplying by 1.15.
Watch out for changes in a row. Raising 100 by 10% gives 110, and then lowering 110 by 10% takes off 11, leaving 99, not 100. The second percentage is taken of a different number. For more on multiplying by decimals like 0.65, see quick decimal calculations.
Answers: (1) 47. (2) 18, half of 36. (3) 18, which is 12 + 6. (4) 24, which is 96 ÷ 4. (5) 34, which is 4 × 8.5. (6) 13, double 6.5. (7) 25%, because 18/72 is 1/4. (8) 60, because 12 × 5 = 60. (9) 187.5, because 150 × 1.25 = 187.5. (10) 255, because 300 × 0.85 = 255.
For more percentage questions that adjust to your level, try the percentages topic in topic practice, or keep your general arithmetic sharp with a round of practice mode and our free maths games.
Find 10% by dividing by 10, then build the percentage you need from it: halve for 5%, double for 20%, and add the pieces together. For 15% of 80, that is 8 plus 4, which is 12.
Work out what percentage of the original you paid, then scale up to 100%. After a 20% discount you paid 80%, so divide the sale price by 8 to get 10%, then multiply by 10.
Yes. Both are x times y divided by 100. So 8% of 50 and 50% of 8 are both 4, and you can pick whichever way round is easier.