11 plus Percentages questions

What a Percentages question looks like

Percentages in the 11 plus are rarely about definitions. Each question puts a percentage next to a real amount, most often money, and asks a child to do something with the pair of them. It is not the same job as rewriting a value from one form into another, and it is not the same job as being handed a fraction and applying it to a quantity: here the percentage itself can be the unknown, and in a good number of questions it is.

The range is wider than “find 25% of this”. Some give a starting price and a reduction. Some give five statements about a set of objects and ask which one is true. Some begin with a small table or a chart, so a value has to be read off first. A few run backwards, giving a part and asking for the whole, or asking what number n makes “n% of £60 = £15” true. It is a sensible place for eleven plus maths practice to settle, because a small set of building blocks answers nearly all of it.

Example one: a percentage of an amount

What is 30% of £70?

Find 10% first. To find 10% of an amount you divide by 10, so 10% of £70 is £7. You want 30%, which is three lots of 10%, so multiply: 3 × £7 = £21.

The answer is £21.

Two of the wrong options are worth a look. £7 is what you get by finding 10% and stopping, which happens when the working is held in the head and the last step slips out of it. £30 is the percentage number written out in pounds, which would only be right if the starting amount were £100.

Example two: what percentage one amount is of another

A bar chart gives the number of items sold at a school fair, with one bar for each kind of item. These are the values it carries:

Sandwiches made up what percentage of the total items sold?

The total is not given, so build it: 20 + 30 + 10 + 20 = 80 items altogether. Sandwiches are 20 of those 80. Write that as a fraction and simplify: 20 out of 80 is a quarter. A quarter is 25%.

The answer is 25%.

The option that catches most children is 20%. The number 20 sits right there against sandwiches, and a count reads very easily as a percentage. It would only be 20% if 100 items had been sold in total. The option 30% is the same slip made with the wrong bar.

Example three: a price that changes twice

A jacket costs £80. Its price is reduced by 20% in a sale. After the sale, the price is increased by 10%. What is the final price?

Take one change at a time, and always work the new percentage out on the newest price. 10% of £80 is £8, so 20% is £16. Take £16 off £80 and the sale price is £64.

Now the rise. It applies to £64, because that is what the jacket costs when the price goes up. 10% of £64 is £6.40, so the final price is £64 + £6.40 = £70.40.

The answer is £70.40.

£80 is there for the child who assumes the two changes cancel out, and £72 for the child who does 20% take away 10% and knocks a single 10% off £80. Neither works, because the second percentage is worked out on a smaller amount than the first.

How to answer it

1. Decide which job the question is asking for. Either you are given a percentage and an amount and have to find the part, or you are given two amounts and have to find the percentage. The two go in opposite directions, so settle it before you start calculating.
2. Check the units match. If one number is in pence and the other in pounds, change one of them first. £4 is 400p, so 80p out of £4 is 80 out of 400, which is a fifth, which is 20%.
3. Build the answer out of 10%. Divide by 10 for 10%, multiply that for 20%, 30% or 70%, halve it for 5%, and divide the original by 2 or by 4 for 50% and 25%. Almost every question in this topic falls out of those few pieces.
4. Handle changes one at a time, in the order the question gives them. A rise or a reduction always applies to the most recent amount, never back to the starting one.
5. Read the last line again before choosing. Different questions want different things: the part, the amount left over, the money saved, or the new price.

Common mistakes

• Writing the percentage out as the answer. £30 for 30% of £70, or 25 for 25% of 80 stickers. The percentage number only equals the answer when the starting amount is 100, and it almost never is.
• Stopping at 10%. A child finds 10% correctly, then answers with it instead of multiplying up. It is one of the most frequent wrong options, and it is a working problem rather than a maths problem: the answer is usually right, one step early.
• Mixing pence and pounds. 50p is not 50% of £2. Turn £2 into 200p first, and 50 out of 200 is a quarter, so the answer is 25%.
• Answering the other half of the question. Giving what is left when the question asked what was spent, or the sale price when it asked for the saving. Word problems are built to make both numbers available and only one of them right.
• Muddling 25% and 50%. Dividing by 2 when the question wants a quarter, or by 4 when it wants a half, is behind a surprising share of the wrong answers on easier questions.

How to practise 11 plus Percentages questions

The thing worth drilling is the 10% habit, because it turns a hard-looking question into two easy ones and it is quick to build. Real prices help: a shop window with 20% off a coat is the same question in the wild, and a child who can say what comes off it while standing there has genuinely learned the skill. Keep sessions short and regular rather than long and occasional, which is the pattern we set out in how much 11 plus practice a child needs each day. When your child gets one wrong, ask which of the two directions the question was going in, because many errors turn out to be that rather than arithmetic. 11+ Daily has a Percentages project alongside the rest of the maths work, on laptop, tablet or phone, and the full list is on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

Questions parents ask