Maths explained
Percentages made simple, with step-by-step worked examples
Percentages made simple: find a percentage of an amount, write one number as a percentage, work out increases and discounts, and solve reverse percentages.
For students. By the Qlive team. . 4 min read.
This guide is for you if you are in roughly Grades 6 to 10 and want percentages to finally make sense. In CBSE, percentages come in Classes 7 and 8 under Comparing Quantities and then appear in profit, loss and interest questions. They are a core part of Key Stage 3, GCSE and IGCSE maths too. You also use them outside school all the time, in discounts, marks and data.
The idea in plain words
Per cent means “out of 100”. So 35% means 35 out of every 100, which is the same as the fraction 35/100 or the decimal 0.35.
That is the whole idea. Every percentage question is really a fraction or decimal question in disguise.
| Percentage | Fraction | Decimal |
|---|---|---|
| 50% | 1/2 | 0.5 |
| 25% | 1/4 | 0.25 |
| 10% | 1/10 | 0.1 |
| 20% | 1/5 | 0.2 |
| 75% | 3/4 | 0.75 |
| 1% | 1/100 | 0.01 |
To change a percentage to a decimal, divide by 100 (move the decimal point two places left). To change a decimal to a percentage, multiply by 100.
Worked examples
Example 1: finding a percentage of an amount
Find 15% of 240.
Method A, using a decimal:
- 15% = 0.15
- 0.15 × 240 = 36
Method B, building from 10% (good without a calculator):
- 10% of 240 = 240 ÷ 10 = 24
- 5% is half of 10%: 24 ÷ 2 = 12
- 15% = 10% + 5% = 24 + 12 = 36
Answer: 36
Example 2: writing one number as a percentage of another
You scored 18 out of 25 in a test. What percentage is that?
- Write it as a fraction: 18/25
- Multiply by 100: 18/25 × 100 = 1800/25 = 72
Answer: 72%
Example 3: percentage increase or decrease
A bicycle cost ₹800 last year and costs ₹920 now. What is the percentage increase?
- Find the change: 920 - 800 = 120
- Divide by the original amount: 120/800 = 0.15
- Multiply by 100: 0.15 × 100 = 15
Answer: a 15% increase
The rule is: percentage change = (change ÷ original) × 100.
Example 4: increasing and decreasing using a multiplier
A multiplier lets you do the change in one step.
- To increase by 20%, you end up with 100% + 20% = 120% of the amount, so multiply by 1.20.
- To decrease by 15%, you end up with 100% - 15% = 85%, so multiply by 0.85.
Increase 450 by 20%: 450 × 1.2 = 540
Decrease 600 by 15%: 600 × 0.85 = 510
Check the second one the long way: 15% of 600 is 90, and 600 - 90 = 510. Same answer.
Example 5: reverse percentage
After a 20% discount, a jacket costs ₹640. What was the original price?
- After a 20% discount, the price is 80% of the original, so the multiplier is 0.8.
- Original × 0.8 = 640
- Original = 640 ÷ 0.8 = 800
Answer: ₹800
Check: 20% of 800 is 160, and 800 - 160 = 640. Correct.
Multipliers at a glance
| Change | Multiplier |
|---|---|
| Increase by 5% | 1.05 |
| Increase by 30% | 1.3 |
| Decrease by 10% | 0.9 |
| Decrease by 25% | 0.75 |
| Decrease by 12% | 0.88 |
Common mistakes and how to avoid them
Dividing by the new amount in percentage change. Always divide by the original. In Example 3, 120 ÷ 920 gives about 13%, which is wrong.
Reverse percentages done forwards. In Example 5, a common wrong answer is 20% of 640 = 128, then 640 + 128 = 768. This fails because the 20% was taken from the original price, not from 640. Divide by the multiplier instead, then check by working forwards.
Thinking equal ups and downs cancel. A 10% rise followed by a 10% fall leaves you below where you started: 100 × 1.1 × 0.9 = 99. Each change works on the new amount.
Decimal point slips. 5% is 0.05, not 0.5. And 0.5 is 50%. If an answer looks far too big or small, check the decimal.
Adding percentages of different amounts. 10% off and then a further 10% off is not 20% off. It is 100 × 0.9 × 0.9 = 81, so 19% off in total.
Try these
- Find 35% of 260.
- Write 42 out of 60 as a percentage.
- A price rises from 250 to 290. Find the percentage increase.
- Decrease 1,500 by 12%.
- After a 25% increase, a price is 1,000. What was it before the increase?
Answers
- 0.35 × 260 = 91. (Or: 10% = 26, so 30% = 78, 5% = 13, and 78 + 13 = 91.)
- 42/60 × 100 = 70%.
- Change = 40. 40/250 × 100 = 16%.
- 1,500 × 0.88 = 1,320.
- 1,000 ÷ 1.25 = 800. Check: 25% of 800 is 200, and 800 + 200 = 1,000.
Still unsure?
Percentages often feel hard because fractions and decimals underneath them are not quite secure. A Qlive teacher can work through it with you one-to-one, starting with a free assessment that finds the exact gap. See how we teach on our maths page, and if fractions are the weak spot, our guide to adding and subtracting fractions is a good place to start.