11 plus Fractions of Amounts questions

What a Fractions of Amounts question looks like

Fractions of Amounts is the type that puts a fraction to work on a real quantity. It hands your child a number of sweets, a length of ribbon or a sum of money, names a fraction of it, and asks what that fraction is worth. That is what separates it from the fraction questions sitting either side of it in an 11 plus maths paper, which simplify and compare fractions, read a fraction off a shaded shape, or rewrite one as a decimal or a percentage. Here the fraction is only the tool, and the quantity is the answer.

The range is wider than the name suggests. The most straightforward questions ask for a unit fraction of a count, such as 1/9 of 45 books. Next come fractions with a number bigger than 1 on top, like 3/8 of 56 crayons, which need one extra step. A large group asks for what is left rather than what was taken, and a larger group again runs two stages, where the second fraction applies to what remains rather than to the number the question started with. A handful work backwards from a part to the whole. A few want the answer written as a fraction instead of as an amount, and a couple set their numbers out in a small table or a Venn diagram. The quantities are counts, centimetres, millilitres, litres, grams and money, up to large round numbers such as £80,000. Every question offers five options, and one is right.

Example one: 3/8 of 56 crayons

A box of 56 crayons is shared out. 3/8 of the crayons are red. How many crayons are red?

The bottom number says how many equal groups to make. Split 56 into 8 groups: 56 divided by 8 is 7, so one eighth is 7 crayons. The top number says how many groups you want, and three of them is 7 times 3, which is 21.

The answer is 21 red crayons.

The wrong option that catches most children is 7. It is a real step in the working, so it feels earned, but it is one eighth and the question asked for three. The other tempting option is 35, the number of crayons that are not red: right sum, wrong question.

Example two: two stages, and the second one is not what you think

A garden centre has 120 plants. On Monday, 1/4 of the plants are sold. On Tuesday, 2/5 of the remaining plants are sold. How many plants are left after Tuesday?

Take Monday first. 120 divided by 4 is 30, so 30 plants go on Monday and 120 take away 30 leaves 90. Now read Tuesday carefully: 2/5 of the remaining plants means 2/5 of 90, not of 120. Split 90 into 5 groups of 18, and two groups is 36 sold, so 90 take away 36 leaves 54.

The answer is 54 plants.

Each wrong option is a stopping point on the way. 90 is where you land if you forget Tuesday. 36 is the number sold on Tuesday, correct but not what was asked. 48 is 2/5 of the original 120, and that is the one to watch, because taking both fractions from the starting number gives an answer that looks reasonable.

Example three: working backwards to the whole

A piggy bank contains some coins. After 3/8 of the coins are spent, 35 coins are left. How many coins were there to start with?

The number you are given is not the whole, so start by naming what 35 is. If 3/8 were spent, then 5/8 are still there, so 35 coins are 5/8 of the pile. Five parts are worth 35, so one part is 35 divided by 5, which is 7. The whole pile is 8 parts: 7 times 8 is 56.

The answer is 56 coins.

The tempting wrong answers are 43 and 40, and both come from the same instinct: take a number out of the fraction and add it to 35. Neither 8 nor 5 is a quantity of coins: they count parts, and a part has to be worked out first.

How to answer it

1. Read to the end and decide what is being asked for: the part taken, the part left, or the whole amount. The words “left”, “remaining”, “not” and “rest” change the answer without changing any of the numbers.
2. Divide the amount by the bottom number of the fraction. That gives one part. If the fraction has a 1 on top, that is the answer and you can stop.
3. Multiply that part by the top number. Divide first and multiply second, because it keeps the numbers small.
4. If there is a second stage, work out what is left after the first stage and apply the second fraction to that new number.
5. Check you are handing over the thing the question asked for, then sense-check the size: a fraction smaller than a half must give an answer smaller than half the amount.

Common mistakes

• Stopping after the divide. For 3/8 of 56 that produces 7, and for 3/5 of £60 it produces £12. The wrong options always include this half-finished answer.
• Giving the part taken when the question wanted the part left. Spend 2/5 of £60 and save the rest: £24 is the spending, £36 is the saving, and only one of them is the answer.
• Applying the second fraction to the starting number. In a two-stage question, 2/5 of what is left is not 2/5 of what you began with. It is the biggest source of lost marks on the harder questions.
• Adding the two fractions when the second acts on a remainder. Working out 3/8 plus 2/5 and taking that share of the original total looks efficient and gives the wrong number.
• Ignoring the units in the options. A question set in metres can offer options in centimetres, so correct working still has to be converted before it matches anything.

How to practise 11 plus Fractions of Amounts questions

Quick recall of times tables is what makes this type feel easy, because “divide by the bottom, multiply by the top” is only fast if the division is instant. Everyday quantities are the cheapest practice there is: half the shopping bill, 3/4 of an hour, 2/5 of a 30-minute journey, asked out loud and answered in the head. When your child gets one wrong, the useful question is not “what is the answer?” but “which number were you meant to end up with?”, because the working is usually sound and the reading is what slipped. That matters more as eleven plus papers move into two-stage questions, where one careless reading undoes correct arithmetic. 11+ Daily has a Fractions of Amounts 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