Maths: Percentages

In a percentages question, you're given a percentage and an amount.

Your job is to work out that percentage of the amount, and pick it from five answers. Per cent means out of a hundred.

In GL's papers a percentage question is one short line. The video above and the worked examples below work through the same questions, with the options in the same order.

The method

Four steps: split the percentage, find one block, build it up, check what's asked.

Worked example

What is 35% of 180?

A. 9 B. 18 C. 35 D. 54 E. 63

1. Split the percentage. Picture the whole amount as 100%, split into ten blocks of 10%. 35% is three of those blocks, and half of one more.
2. Find one block. 10% of an amount is the amount ÷ 10. 180 ÷ 10 = 18, so every whole block is worth 18. 18 is option B, but that's only one block, so B is out.
3. Build it up. Add the blocks you need. Three blocks of 18 make 30%: 3 × 18 = 54. 54 is option D, but it stops at 30%. The 5% block is still missing, so D is out. 5% is half of 10%, so the half block is half of 18, which is 9. 9 on its own is option A, just the half block, so A is out too. Now put them together: 54 + 9 = 63.
4. Check what's asked. Look back at the question, and check your answer makes sense. The question asks for 35% of 180. 35 on its own is just the percentage, so C is out. And 35% is less than half. Half of 180 is 90, and 63 is less than 90, so it makes sense. So the answer is E.

Answer: E — 63 (35% of 180 = 54 + 9 = 63)

A second worked example

Sometimes it's the other way round: what percentage is one amount of another? The same four steps work here too.

Adam scores 3 out of 20 in a spelling test. What percentage is that?

A. 3% B. 6% C. 15% D. 83% E. 85%

1. Split the percentage. This time, the whole test is 100%, split into 20 blocks, one for each mark.
2. Find one block. 100 ÷ 20 = 5, so each mark is worth 5%. 6% doubles the 3, as if each mark were only 2%, so B is out. 3% counts each mark as 1%, as if the test were out of 100, so A is out too.
3. Build it up. Adam scored 3 marks, so that's three blocks: 3 × 5 = 15, so it's 15%.
4. Check what's asked. The question asks about the marks he scored. 85% is the 17 marks he missed, so E is out. And 3 marks is less than half the test, so the answer must be less than 50%. 83% is far too big, so D is out. So this one is C.

Answer: C — 15% (100% ÷ 20 = 5%, and 3 × 5% = 15%)

Things to watch out for

1. 10% is a step, not the answer. It's the first block you find, so it's easy to stop there. In the first worked example, B was 18, just one block, when 35% needs three and a half.
2. Keep the percentage and the amount apart. Each number has its own job: the percentage says how many blocks to take, and the amount is what you split. In the first worked example, C was 35, the percentage copied straight across.
3. Same units first. Pence with pence, pounds with pounds. What percentage of £2 is 40p? £2 is 200p. 10% of that is 20p, so 40p is two blocks, which is 20%. 40% would only be right if the whole were £1.
4. Sense-check with a half or a tenth. What is 30% of 60? A tenth of 60 is 6, and half of 60 is 30. 30% is between a tenth and a half, so the answer must be between 6 and 30. 180 is more than the whole amount. Only 18 fits, and it's three lots of 6.

Related

• The complete 11+ question-type guide
• Maths: Fractions — find the whole, cut it into equal parts
• Maths: Ratio and Proportion — find what one part is worth, then scale
• Maths: Measures — make the units the same before you work

All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.