Ross MackellUK-qualified primary teacher · 10 min read

What's 35% of 80?

If your first thought was "where's my calculator?", you're not alone. Most parents I speak to feel exactly the same. But your child is expected to answer that in Year 6, on paper, without a calculator.

The good news: there's a method that makes it surprisingly easy. Once you see it, you'll never reach for a calculator for percentages again. (The answer is 28, and by the end of this guide you'll be able to work it out in about ten seconds.)

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you exactly how your child is taught percentages: the four percentages that unlock all the others, how to build any percentage from them, how to work out discounts, and the three mistakes children make most.

What a percentage actually is

"Per cent" means "out of 100". That's it. 35% means 35 out of every 100.

So when we find 35% of 80, we're really asking: if 80 was split into 100 equal parts, how much would 35 of those parts be?

You don't need to actually split anything into 100 parts. That's what the big four are for.

When children learn percentages

• Year 5: children meet the % symbol and learn that per cent means "out of 100". They write percentages as fractions and decimals, and learn the equivalents for halves, quarters and fifths. This is set out in the national curriculum.
• Year 6: they find percentages of amounts (like 15% of 360), use percentages to compare things, and switch confidently between fractions, decimals and percentages.
• On the SATs: percentages of amounts turn up on the Year 6 SATs arithmetic paper, and in the reasoning papers as word problems.

Percentages sit near the top of the maths ladder. They rely on skills your child learned earlier: halving, dividing by 10 and 100, and fractions. If those are wobbly, percentages will be too.

The big four: 50%, 25%, 10% and 1%

Here's the secret. Your child only needs four percentages. Every other percentage is built from these.

If your child can do these four quickly and confidently, they can do almost any percentage question in primary school. And notice: it's just halving and dividing by 10 and 100. Skills they already have.

How to work out any percentage

Now we build. The method is the same every time: break the percentage into pieces you know, find each piece, then add them up.

35% of 80

1. Break it up: 35% = 10% + 10% + 10% + 5%.
2. Find 10%: 80 ÷ 10 = 8. Three lots of 10% is 24.
3. Find 5%: half of 10%. Half of 8 is 4.
4. Add them: 24 + 4 = 28.

15% of 60

15% = 10% + 5%. 10% of 60 is 6, and 5% is half of that, 3. So 6 + 3 = 9.

75% of 240

75% = 50% + 25%. Half of 240 is 120, and a quarter is 60. So 120 + 60 = 180.

12% of 300

12% = 10% + 1% + 1%. 10% of 300 is 30, and 1% is 3. So 30 + 3 + 3 = 36.

And the SATs-style one: 15% of 360

10% of 360 is 36. 5% is half of that, 18. So 36 + 18 = 54.

Every single one used the same idea. Your child doesn't need to memorise a different method for every percentage. Break it into pieces you know.

Fractions, decimals and percentages

In Year 6, children are expected to know these equivalents by heart. They're worth sticking on the fridge.

The link between them is always "out of 100". 3/4 is the same as 75/100, which is 75%, which is 0.75.

Discounts and "what percentage is...?"

Working out a discount

1. Find 20%: 10% of 60 is 6, so 20% is 12.
2. Take it away: £60 − £12 = £48.

This is where children slip up. They find the 20%, write £12, and stop. Always ask: is that the discount, or the price you pay? This is a brilliant one to practise for real next time you're in the shops.

What percentage is 18 out of 40?

This is the one that turns up as a test score. 18 out of 40 on a spelling test: what percentage is that?

1. Write it as a fraction: 18/40.
2. Simplify if it helps: 40 doesn't go into 100 neatly, so halve both numbers first. 18/40 = 9/20.
3. Make the bottom 100: 20 × 5 = 100, so multiply the top by 5 too. 9/20 = 45/100.
4. Read it off: 45 out of 100 is 45%.

If percentages are coming up in a SATs practice paper, these are exactly the two question types to practise.

3 mistakes and what to say

Mistake 1: Dividing by the percentage

• What it looks like: working out 35% of 80 by doing 80 ÷ 35.
• What to say: "We divide by 10 or 100 to find a piece. Which pieces make 35%?"

Mistake 2: Mixing up 5% and 50%

• What it looks like: 5% of 80 written as 40.
• What to say: "5% is tiny, it's half of 10%. 50% is half of the whole thing. Should the answer be small or big?"

Mistake 3: Stopping at the discount

• What it looks like: "20% off £60" answered as £12.
• What to say: "Is that what you save, or what you pay? What does the question actually want?"

And the quick sense check that catches all three: 10% is always a small piece, and 50% is always half. If an answer is bigger than the starting amount for anything under 100%, something's gone wrong.

A 5-minute practice routine

Same three steps I use for every method: watch, copy, practise.

1. Watch: pick one number, like 60 or 200. You find the big four for it, saying it out loud. "Half is... a quarter is... 10% is... 1% is..."
2. Copy: your child does the big four for a new number.
3. Practise: your child builds two more from it, like 35% and 15%.

Real life works brilliantly too: sale signs, the battery percentage on a phone, test scores. Here's a set to get you going.

For more SATs-style practice, the government publishes free KS2 past papers.

Frequently asked questions

How do you work out a percentage of a number without a calculator?

Start with the big four: 50% (halve it), 25% (halve it again), 10% (divide by 10) and 1% (divide by 100). Then build the percentage you need from those pieces and add them up. For example, 35% of 80 is 10% + 10% + 10% + 5%, which is 8 + 8 + 8 + 4 = 28.

How do you work out 10% of a number?

Divide the number by 10. 10% of 80 is 8, 10% of 350 is 35, and 10% of 6 is 0.6.

How do you work out what percentage one number is of another?

Write it as a fraction, then change it so the bottom number is 100. For 18 out of 40: 18/40 = 9/20 = 45/100, which is 45%.

How do you work out a discount?

Find the percentage off, then subtract it from the original price. For 20% off £60: 20% of £60 is £12, so you pay £60 − £12 = £48.

What year do children learn percentages?

Children are introduced to percentages in Year 5, where they learn that per cent means "out of 100". In Year 6 they find percentages of amounts, and percentages come up on the KS2 SATs.