11 plus Ratio & Scaling questions

What a Ratio & Scaling question looks like

Ratio is one of the most frequently tested ideas in 11 plus maths, and it asks a child to hold two numbers in a relationship rather than work on one at a time. Here is what separates it from the fractions and percentages topics next door: those name the share to take of an amount you already have, while a ratio question describes how something is split without naming anybody’s share directly, so the value of one part has to be found first, and often the total is the unknown.

The questions come in a few recognisable shapes. Some share a total between two or three named children. Some mix to a recipe: squash and water, blue and yellow paint, sand and cement. Some scale up, so a dish for 4 people becomes a dish for 12 and every ingredient is multiplied by 3. Some run backwards, giving one person’s share, or only the difference between two shares, and asking for the total. A few sit outside that: the cost of 9 bread rolls when you know the cost of 6, a map scale, and reading two values off a chart to write the ratio between them in its simplest form. The hardest ones share the total and then add a step, such as one child giving half of their tokens away. One method covers nearly all of it, which makes it a good topic for eleven plus practice to settle on.

Example one: sharing a total

Petra and Quinn share £72 in the ratio 5:4. How much does Petra receive?

The ratio says the money is cut into 5 parts for Petra and 4 parts for Quinn, so first find how many parts there are altogether: 5 + 4 = 9. Now share the money between those 9 parts: £72 divided by 9 is £8. Petra has 5 parts, which is 5 lots of £8.

The answer is £40.

Two wrong answers are worth naming. £32 is Quinn’s share, taken by a child who worked correctly and read the wrong name. £36 is half of £72, chosen by a child who saw “share” and split it evenly, which is exactly what the ratio is telling you not to do.

Example two: working back from one share

Nina and Omar share some money in the ratio 3:5. Omar receives £40. How much money is shared altogether?

The total is missing, so the one-part step has to come from Omar. The ratio is Nina first, Omar second, so Omar has 5 parts. Those 5 parts are worth £40, so one part is £40 divided by 5, which is £8. Nina has 3 parts, which is £24. Altogether they share £24 + £40 = £64.

The answer is £64.

£80 tempts a lot of children, because doubling the £40 feels like finding the whole. It would only be right if the shares were equal, and 3:5 says they are not. £24 tempts a different child: the working was right all the way to Nina’s share, and then that got written down instead of the total.

Example three: a mixture with no total given

To make orange paint, Uma mixes red and yellow in the ratio 3:5. She has 18 litres of red paint. What is the maximum amount of orange paint she can make?

Red is named first, so red is 3 parts. Those 3 parts are 18 litres, so one part is 6 litres. Yellow is 5 parts, so Uma needs 5 lots of 6 litres, which is 30 litres of yellow. The orange paint is the red and the yellow together: 18 + 30.

The answer is 48 litres.

30 litres is the yellow on its own, and it catches anyone who finds the missing ingredient and stops there. 54 litres comes from multiplying the 18 litres of red by its own ratio number, 3, muddling a number of parts with an amount of paint.

How to answer it

1. Write down which name goes with which number. The order in the ratio follows the order in the sentence, so in “Nina and Omar share money in the ratio 3:5” Nina has 3 and Omar has 5. Getting it the wrong way round lands on one of the options every time.
2. Decide what you have been given: the whole total, one person’s share, or the difference between two shares. That is the only real decision in the question.
3. Find what one part is worth. Given the total, add the ratio numbers and divide the total by that. Given one share, divide it by that person’s number of parts. Given the difference, divide it by the difference between the ratio numbers.
4. Multiply back up for whatever was asked. One part times the right number of parts gives a share, and one part times the total number of parts gives the whole.
5. Read the last line again before choosing. It might want a share, the total, how much more one person got, or what is left after somebody spends some, and all four are usually in the options.

Common mistakes

• Dividing by one of the ratio numbers instead of the total. For £72 in the ratio 5:4, dividing by 5 or by 4 rather than by 9. Add the parts first, every time.
• Answering with the other person’s share. The working is right and the name is wrong. Underlining the name asked about before starting fixes most of these.
• Stopping at the value of one part. £8, or 5 litres, or 8 kg is found correctly and then written down as the answer. Right answer, one step early.
• Adding a ratio number rather than the scaled amount. If 20 kg of sand is 4 parts, one part is 5 kg, so the mortar weighs 20 + 5 = 25 kg. Answering 21 or 24 means the 1 or the 4 got added instead.
• Assuming an even split once a number appears. Doubling the one share you are given, as though the ratio were 1:1, is behind a lot of the wrong answers on the backwards questions.

How to practise 11 plus Ratio & Scaling questions

The habit worth building is saying “one part is worth …” out loud before anything else, because almost every question here falls out of that single line, forwards or backwards. Cooking is the honest version of it at home: halving a recipe for 4, or making it for 12, is the same skill with real consequences. 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 what one part was worth: the error is nearly always before that line. 11+ Daily has a Ratio & Scaling 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