"What's three quarters of 20?" It sounds simple. But ask a room of Year 4s and you'll get 15, 60, 23, and at least one child who just stares at you. Finding a fraction of an amount is one of those skills that looks easy to adults and catches out a huge number of children.
The good news: there is one rule, it always works, and once your child understands why it works, they'll stop mixing it up. It's also a question that turns up on the Year 6 SATs arithmetic paper every single year, so it's worth getting right.
I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you the method, a simple picture that makes it click, worked examples from easy to SATs level, the mistakes I see most often, and a 10-minute practice routine with answers.
Quick answer: to find a fraction of an amount, divide by the bottom number, then multiply by the top number. For 34 of 20: 20 ÷ 4 = 5, then 5 × 3 = 15. The bottom number tells you how many equal parts to split into. The top number tells you how many of those parts you want.
In this guide
What your child needs first
Fractions of amounts is really a division skill wearing a fractions costume. Your child needs:
- Division facts. If they know 4 × 5 = 20, they need to know 20 ÷ 4 = 5 just as quickly. Times tables come first: how to learn times tables fast.
- A written division method for bigger numbers. In Year 5 and 6 that's usually the bus stop method.
- What a fraction actually is. That 14 means one of four equal parts.
In the national curriculum, children start finding fractions of a set of objects in Year 3, and by Year 4 they're expected to solve problems that use harder fractions to work out quantities. By Year 6, they'll meet questions like 38 of 96 on the SATs arithmetic paper.
What does "a fraction of an amount" mean?
Before any rule, I always start with a picture. Here's 20 split into 4 equal parts. Each part is worth 5.
This is called a bar model. 34 of 20 is three of the four parts: 5 + 5 + 5 = 15.That's all a fraction of an amount is: split the amount into equal parts, then count how many parts you need. The method is just the quick way of doing that.
Step 1: unit fractions (one part)
A unit fraction has a 1 on top, like 12, 13 or 15. You only want one part, so there's only one step: divide.
Example 1: 13 of 12
- The bottom number is 3, so split 12 into 3 equal parts.
- 12 ÷ 3 = 4.
That's it. You want one part, and one part is 4.
Example 2: 18 of 56
- Split 56 into 8 equal parts.
- 56 ÷ 8 = 7.
If your child gets stuck here, it's almost always the division fact, not the fraction. Ask "what times 8 makes 56?" instead.
Step 2: non-unit fractions (more than one part)
Now the top number is bigger than 1, like 34 or 25. There's one extra step: after you've found one part, multiply by how many parts you want.
Example 3: 34 of 20
- Divide by the bottom: 20 ÷ 4 = 5. One quarter is 5.
- Multiply by the top: 5 × 3 = 15. Three quarters is 15.
Example 4: 25 of 35
- Divide by the bottom: 35 ÷ 5 = 7. One fifth is 7.
- Multiply by the top: 7 × 2 = 14.
I get children to say the middle step out loud every time: "One fifth is 7, so two fifths is 14." It stops them skipping a step and it makes the answer easy to sense-check.
Fractions of amounts falls apart if division is shaky. Times tables, division and fractions are all part of the 15 core skills every child aged 7 to 11 needs.
My free guide for parents shows all 15 core skills in order, so you can see exactly which one is holding your child back.
Get the free 15 Core Skills guide →Bigger numbers and SATs-style questions
The method doesn't change with bigger numbers. Only the division gets harder, so your child will need a written method instead of a times table fact.
Example 5: 38 of 96
- Divide by the bottom: 96 ÷ 8 = 12. (Use the bus stop method if it's not a known fact.)
- Multiply by the top: 12 × 3 = 36.
Example 6: 37 of 245
- Divide by the bottom: 245 ÷ 7 = 35.
- Multiply by the top: 35 × 3 = 105.
This is a typical Year 6 SATs-style question. Notice it's really testing division: if your child can do 245 ÷ 7 confidently, the rest is easy.
Example 7: 14 of £3
- £3 doesn't split into 4 nicely, so change it to pence: £3 = 300p.
- Divide by the bottom: 300 ÷ 4 = 75p.
Money and measures questions often look harder than they are. Converting to a smaller unit first (pence, grams, centimetres) usually makes the numbers friendlier.
4 common mistakes and how to fix them
Mistake 1: Dividing by the top number
For 34 of 20, your child does 20 ÷ 3. It doesn't work, and they get stuck with a remainder.
The fix: go back to the bar model. "How many equal parts are there?" The bottom number. Always. I teach it as "the bottom number is the number of boxes you draw".
Mistake 2: Multiplying instead of dividing
They do 20 × 4 = 80, then 80 × 3 = 240. A fraction of something is always smaller than the whole (for fractions less than 1), so this should ring alarm bells.
The fix: before calculating, ask "Will the answer be bigger or smaller than 20?" If they predict smaller, they'll catch themselves.
Mistake 3: Stopping after the divide
For 34 of 20 they write 5. That's one quarter, not three.
The fix: the "say the middle step out loud" habit. "One quarter is 5, so three quarters is..." It's almost impossible to stop at 5 if they've said that sentence.
Mistake 4: The division itself goes wrong
Plenty of children get the method completely right and then make a slip in 245 ÷ 7.
The fix: this is a division problem, not a fractions problem. If it keeps happening, spend a week on short division. That's where the marks are really being lost.
A 10-minute practice routine
Same three steps I use for every skill: watch, copy, practise.
- Watch: do one yourself, out loud. "Three quarters of 20. Divide by the bottom: 20 divided by 4 is 5. One quarter is 5, so three quarters is 15."
- Copy: your child does a very similar one, saying each step out loud.
- Practise: three or four on their own, then check together.
| Question | What it practises | Answer |
|---|---|---|
| 1/5 of 30 | Unit fraction, one step | 6 |
| 1/8 of 56 | Harder division fact | 7 |
| 2/3 of 18 | Non-unit, two steps | 12 |
| 3/4 of 36 | Non-unit, two steps | 27 |
| 5/6 of 42 | Bigger top number | 35 |
| 3/5 of 125 | 3-digit amount | 75 |
| 2/7 of 168 | Bus stop division first | 48 |
| 3/4 of £2 | Money: change to pence | £1.50 |
Work down the table over a week or two. Only move on when they're getting three in a row right. Ten minutes, a few times a week, is plenty.
Keep going
Frequently asked questions
How do you find a fraction of an amount?
Divide the amount by the bottom number (the denominator), then multiply the answer by the top number (the numerator). For example, 3/4 of 20: 20 ÷ 4 = 5, then 5 × 3 = 15.
How do you find a fraction of a number with bigger numbers?
The method is exactly the same: divide by the denominator, then multiply by the numerator. With bigger numbers, use a written method such as short division (the bus stop method) for the divide step. For example, 3/7 of 245: 245 ÷ 7 = 35, then 35 × 3 = 105.
What year do children learn fractions of amounts?
In England, children start finding fractions of a set of objects in Year 3. In Year 4 they solve problems with harder fractions, and fractions of amounts appear regularly on the Year 6 KS2 SATs arithmetic paper.
Why do you divide by the denominator?
The denominator tells you how many equal parts the whole is split into. Dividing by it tells you how big one part is. The numerator then tells you how many of those parts you want, which is why you multiply by it next.
Is finding a fraction of an amount the same as multiplying fractions?
Yes, in a way. 3/4 of 20 means the same as 3/4 × 20. Dividing by 4 and multiplying by 3 is just the quickest way to work it out. Children usually learn it as "divide by the bottom, times by the top" first, then meet the link to multiplying fractions in Year 6.
Get all 15 core skills in one place
Fractions of amounts are easy marks once division is secure. The 15 core skills are the written methods and facts every child aged 7 to 11 needs to master to succeed in maths.
My free guide for parents shows all 15, in order, so you can see exactly where your child is and what comes next.
Get the free 15 Core Skills guide →Sources and further reading
- Department for Education, National curriculum in England: mathematics programmes of study (fractions in Years 3 and 4)
- Standards and Testing Agency, Key stage 2 mathematics test framework
- Ross Mackell, Teacher's Perspective on YouTube
