Percentages of an Amount
Finding a percentage of an amount means taking a stated share of that amount. We will start with halves, quarters and tenths, then build up to less familiar percentages.
Use the early examples to build confidence. The final two examples offer further practice for both tiers.
What does a percentage of an amount mean?
Remember from Fractions, Decimals & Percentages: per cent means “out of 100”. The symbol % means “per cent”.
The complete amount is 100%. If we split it into 100 equal shares, 1% is one share. For example, 30% means 30 of those equal shares.
Some familiar shares have easier names: 50% is , 25% is , 10% is and 1% is .
So 50% of £20 means half of £20.
The same percentage can give different answers for different amounts. Half of £20 is £10, but half of £40 is £20. Always identify the whole amount first.
Example Question:
Find 15% of 80.
Could you find 10% and 5% first, then combine them? Example 4 shows this method.
Exam Tip
Underline the percentage and the amount it applies to.
Estimate before calculating. For a positive amount, a percentage between 0% and 100% gives less than the whole.
Keep the original unit in your answer: pounds, grams, metres or the named objects.
Method — Start with Familiar Percentages
These benchmark percentages are useful starting points. Choose the one that makes the question easiest.
| Percentage | Mental method |
|---|---|
| 50% | Find one half: divide by 2. |
| 25% | Find one quarter: divide by 4. |
| 10% | Find one tenth: divide by 10. |
| 5% | Find 10%, then halve that answer. |
| 1% | Find one hundredth: divide by 100. |
You can combine shares of the same amount:
15% = 10% + 5%
35% = 30% + 5%
75% = 50% + 25%
There may be several sensible methods. For 75%, you could instead find 25% and multiply that answer by 3.
Worked Examples
Example 1 — Find 50% using a half
Find 50% of £20.
50% means one half. Divide the amount by 2:
£20 ÷ 2 = £10
50% of £20 = £10
The shaded half of the opening bar shows this answer.
Example 2 — Find 25% using a quarter
Find 25% of 40.
25% is one quarter because four lots of 25% make 100%. Split 40 into four equal parts:
40 ÷ 4 = 10
25% of 40 = 10
Example 3 — Find 10%, then 5%
Find 10% and 5% of 60.
10% is one of ten equal parts. Divide 60 by 10:
60 ÷ 10 = 6
10% of 60 = 6
5% is half of 10%. Halve the answer 6:
6 ÷ 2 = 3
5% of 60 = 3
Example 4 — Combine known percentages
Find 15% of 80.
Break 15% into 10% + 5%.
First find 10%:
80 ÷ 10 = 8
Then find 5% by halving 8:
8 ÷ 2 = 4
Add the two shares:
8 + 4 = 12
15% of 80 = 12
Here are two other useful combinations for the same amount, 80:
| Percentage | Build it from known shares |
|---|---|
| 35% | 30% gives 3 × 8 = 24. Add the 5% share, 4: the answer is 28. |
| 75% | 50% gives 40 and 25% gives 20. Add them: the answer is 60. |
Example 5 — Find 1%, then scale up
Find 17% of £300.
The whole £300 represents 100%. Divide it into 100 equal shares:
£300 ÷ 100 = £3
1% of £300 = £3
17% means seventeen of those 1% shares. Multiply the value of one share by 17:
17 × £3 = £51
17% of £300 = £51
This is the unitary method: find one equal share first, then find as many shares as you need.
It works for any percentage. You do not have to use it when a quicker method is available, such as halving to find 50%.
Example 6 — Use a decimal multiplier
A multiplier is simply a number you multiply by. To find a percentage of an amount, use the percentage written as a decimal.
From the earlier conversion lesson, 20% = = 0.20.
Multiplying by 0.20 takes twenty hundredths of the amount. In this calculation, the word “of” means multiply:
20% of 80 = 0.20 × 80
20% of 80 = 16
Now use a calculator to find 23% of £68.
First convert the percentage to a decimal by dividing its number by 100:
23 ÷ 100 = 0.23
So 23% = 0.23. Multiply the amount by this decimal:
0.23 × £68 = £15.64
23% of £68 = £15.64
The answer is £15 and 64p. Do not multiply by 23, which would find 23 whole amounts.
Example 7 — A GCSE-style quantity problem
There are 80 students in a year group. 35% walk to school. How many students is this?
The whole amount is 80 students. Find 30% + 5%.
10% of 80 = 8
30% of 80 = 3 × 8 = 24
5% of 80 = 8 ÷ 2 = 4
24 + 4 = 28
28 students walk to school.
A calculator gives the same result: 0.35 × 80 = 28.
Example 8 — Further practice: a decimal percentage
Find 2.5% of £360. A percentage can contain a decimal.
2.5% is half of 5%, so we can halve twice:
10% of £360 = £36
5% of £360 = £36 ÷ 2 = £18
2.5% of £360 = £18 ÷ 2 = £9
2.5% of £360 = £9
With a calculator, convert the percentage carefully:
2.5 ÷ 100 = 0.025
0.025 × £360 = £9
Both methods give the same answer.
Example 9 — Further practice: more than 100%
Find 120% of 250 ml. The unit ml means millilitres.
100% is one whole amount. 120% means 100% + 20% of that same amount.
100% of 250 ml = 250 ml
10% of 250 ml = 25 ml
20% of 250 ml = 2 × 25 ml = 50 ml
250 ml + 50 ml = 300 ml
120% of 250 ml = 300 ml
This must be greater than 250 ml because the requested percentage is greater than 100%.
Percentages in bills and tax
VAT is a tax added to a price when the question states that VAT is not yet included. First identify the amount on which the percentage is charged.
Worked bill: two items cost £35 each before VAT and delivery costs £18 before VAT. The question gives VAT of 20% on the whole bill. Subtotal: 2 × £35 + £18 = £88. VAT: 0.20 × £88 = £17.60. Total payable: £88 + £17.60 = £105.60.
Income tax is deducted from income. The taxable amount may be smaller than the full income. In this invented rule, monthly pay is £2000, the first £1250 is tax-free, and the rest is taxed at 20%. Taxable pay is £2000 − £1250 = £750. Tax is 0.20 × £750 = £150, leaving £1850 after this tax. Always use the allowance and rates supplied in the question; these are practice figures, not current tax rules.
Quick practice — A bill is £65 before VAT at a stated rate of 20%. Separately, £1800 pay has a £1200 tax-free allowance and a stated 15% tax on the remainder. Find the bill total and the pay after this tax.
VAT is 0.20 × £65 = £13, so the bill is £78.
Taxable pay is £1800 − £1200 = £600. Tax is 0.15 × £600 = £90, leaving £1710.
Choose an efficient route
Familiar share? Use a half, quarter or tenth.
Easy combination? Build the percentage from shares you already know.
Less familiar percentage? Find 1% and scale up, or use a decimal multiplier if a calculator is allowed.
All these methods find the same share. Choose a method you can explain and check.
Check that your answer makes sense
Estimate before accepting a calculator answer.
For 23% of £68, compare with 25%. A quarter of £68 is £17. The answer should be slightly below £17. £15.64 fits.
For positive amounts, 10% is less than the whole. For example, 10% of £80 is £8.
50% should be half of the whole. 5% should be half of the 10% answer.
A percentage above 100% gives more than the whole. For example, 120% of 250 ml is greater than 250 ml.
Check the unit too. Finding a percentage changes the amount, not pounds into pence or grams into kilograms.
Express one amount as a percentage of another
Finding a percentage of an amount gives the part. Sometimes the part and the whole are known, and you need the percentage instead. First write part ÷ whole, then multiply by 100.
Worked example — a test score
A student scores 18 out of 24 marks. The fraction of the available marks is .
18 ÷ 24 = 0.75
0.75 × 100 = 75
The score is 75%.
The whole must be the amount named in the question. “18 as a percentage of 24” is different from “24 as a percentage of 18”. Make the units match before dividing.
Quick practice — what percentage of 2 kg is 350 g?
2 kg = 2,000 g. The whole is 2,000 g, not 2 g.
350 ÷ 2,000 = 0.175. Multiply by 100: 17.5%.
Think Like a Mathematician
Why is 30% of an amount three times as much as 10% of that same amount?
Split the whole into ten equal parts. Each part is 10%. Three of those parts make 30%.
The parts are equal, so three parts have three times the value of one part.
For 80, one tenth is 8. Three tenths are 3 × 8 = 24. This is why we can build larger percentages from smaller known shares.
Common mistakes to avoid
Using 20 instead of 0.20. 20% is twenty hundredths, not twenty wholes. Divide the percentage number by 100 to get the multiplier.
Confusing 10% with 0.1%. 10% is 0.1 as a decimal. But 0.1% is 0.001. Keep track of the % sign.
Dividing the wrong number. To find 10%, divide the amount by 10. To find 1%, divide the amount by 100.
Combining the wrong shares. 15% is 10% + 5%, not 10% + 15%. Check the percentages add to your target.
Forgetting the unit. A percentage of a price is still money. A percentage of a mass is still a mass.
Assuming every answer is smaller. This works for percentages between 0% and 100% of a positive amount. Percentages above 100% give more than the whole.
Try it yourself
Start with the familiar percentages, then try the longer questions. Show your method and include units where given. Questions 10–11 are further practice for both tiers.
1. Find 50% of £36.
50% is one half:
£36 ÷ 2 = £18
50% of £36 = £18
2. Find 25% of 28.
25% is one quarter. Split 28 into four equal parts:
28 ÷ 4 = 7
25% of 28 = 7
3. Find (a) 10% of 90 and (b) 5% of 90.
For 10%, divide by 10:
90 ÷ 10 = 9
(a) 10% of 90 = 9
For 5%, halve the 10% answer:
9 ÷ 2 = 4.5
(b) 5% of 90 = 4.5
4. Find 1% of £250.
1% is one of 100 equal shares:
£250 ÷ 100 = £2.50
1% of £250 = £2.50
£2.50 means two pounds and fifty pence.
5. Find 15% of 160 without a calculator.
Use 10% + 5%.
10% of 160 = 16
5% of 160 = 16 ÷ 2 = 8
16 + 8 = 24
15% of 160 = 24
6. Use the unitary method to find 13% of £250.
Find 1% first:
£250 ÷ 100 = £2.50
Then take thirteen equal shares:
13 × £2.50 = £32.50
13% of £250 = £32.50
7. Use a decimal multiplier to find 18% of £45.
Convert 18% to a decimal:
18 ÷ 100 = 0.18
Multiply the amount by 0.18:
0.18 × £45 = £8.10
18% of £45 = £8.10
Write £8.10 for eight pounds and ten pence.
8. A school has 64 pupils on a trip. 75% need a packed lunch. Lunches come in packs of 6. How many packs are needed?
Find the number of lunches first. Use 50% + 25%.
50% of 64 = 32
25% of 64 = 16
32 + 16 = 48
So 48 pupils need lunches. Each pack contains 6:
48 ÷ 6 = 8
8 packs are needed.
9. Find 32% of 350 g. The unit g means grams.
32% = 0.32
0.32 × 350 g = 112 g
32% of 350 g = 112 g
A mental check: 30% gives 105 g and 2% gives 7 g. Together they give 112 g.
10. Further practice: find 12.5% of £72.
12.5% is half of 25%.
25% of £72 = £72 ÷ 4 = £18
12.5% of £72 = £18 ÷ 2 = £9
12.5% of £72 = £9
A calculator check uses 12.5 ÷ 100 = 0.125.
0.125 × £72 = £9
11. Further practice: find 150% of 80 cm. The unit cm means centimetres.
150% is 100% + 50% of the same amount.
100% of 80 cm = 80 cm
50% of 80 cm = 40 cm
80 cm + 40 cm = 120 cm
150% of 80 cm = 120 cm
This is greater than the original 80 cm, as expected.
Frequently Asked Questions
What does “of” mean here?
It asks you to take the stated share of the amount. In a calculation, multiply the amount by the percentage written as a fraction or decimal.
Must I always find 1% first?
No. The unitary method is useful, but a benchmark can be quicker. For example, find 50% by halving.
Why does the decimal multiplier work?
20% means twenty hundredths, which is 0.20. Multiplying an amount by 0.20 takes twenty hundredths of it. It is the same as dividing the amount by 100, then multiplying by 20.
Can two different methods both be correct?
Yes. To find 75%, you can add the 50% and 25% shares, or find 25% and multiply by 3.
Can percentages work both ways?
Yes. For example, 25% of 16 and 16% of 25 are both 4.
The first calculation is 25 × 16 ÷ 100. The second is 16 × 25 ÷ 100. Swapping the order of the multiplication does not change the answer.
Should I round every money calculation?
Keep the full value while working. Give a final money answer in pounds and pence, rounding to the nearest penny if needed. The money examples on this page give exact penny amounts.
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