What does a child have to do to find a fraction of a quantity in the 11+?

Calculate one unit or non-unit fraction of a quantity. It is one of 55 named maths skills in the 11+, in the fractions, decimals and percentages strand, and this page carries 2 interactive exercises that practise it.

What is the trap in an 11+ find a fraction of a quantity question?

One part of the bar is not the same as the shaded part. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on find a fraction of a quantity?

Point at the next move rather than explaining the whole rule. Split 128 into 8 equal groups first, then take 3 of those groups - do not stop after one group.

What is not part of find a fraction of a quantity in the 11+?

The skill map draws the line here: Excludes chained operations. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside find a fraction of a quantity?

The fractions, decimals and percentages strand holds 9 skills that are tested together, and the pages next to find a fraction of a quantity are find a percentage of a quantity, identify a represented fraction and locate an equivalent value. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise find a fraction of a quantity for free?

Use Quantity Split and Area Grid, embedded on this page. They are the exercises the skill map attaches to find a fraction of a quantity, they run in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Maths · Fractions, decimals and percentages

Find a fraction of a quantity

Calculate one unit or non-unit fraction of a quantity.

Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.

Practise it now

Build 60% of 60 marbles on the board, then work out 60% of 40 without it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Taking $\frac{3}{8}$ of an amount

What is $\frac{3}{8}$ of 128?

Each of the 8 sections of this bar is worth 16, and 3 sections are shaded.

A bar cut into 8 equal parts, with 3 of them shaded.

Answer: 48

How you get there

Dividing 128 by 8 gives 16 in each part, and 3 parts means 3 x 16, which equals 48.

Why the other answers tempt

One part of the bar is not the same as the shaded part.

If they are stuck, say this

Split 128 into 8 equal groups first, then take 3 of those groups - do not stop after one group.

Now do it live in Quantity Split

How each of these 2 exercises teaches it

Quantity Split

Build 60% of 60 marbles on the board, then work out 60% of 40 without it.

Per cent means "out of a hundred", so 60% is $\frac{60}{100}$ . Both numbers divide by 20, which leaves $\frac{3}{5}$ - the same share, with far fewer groups to cut. The bottom number is how many equal groups the whole pile is cut into and the top number is how many of those groups you keep. $40 \div 5 = 8$ , so one group holds 8 marbles, and 3 groups hold $3 \times 8 = 24$ . The groups add straight back up to 40 with nothing left over.

Step 1. Cut it up. Cut 60 marbles into 5 equal groups.
Step 2. Take your share. Now light up 3 of those 5 groups.
Step 3. A new pile. The board is covered. What is 60% of 40 marbles?

What to say if they get stuck

60% cancels: both numbers divide by 20, leaving $\frac{3}{5}$ . Cut the pile into 5 groups, not 100.
$40 \div 5 = 8$ , so each group holds 8 marbles.
Now take 3 of those groups: $3 \times 8$ .

Open Quantity Split on its own page to share it

Area Grid

Slide the coral band to $\frac{2}{3}$ and the teal band to $\frac{3}{4}$ . Where they cross is $\frac{2}{3} \times \frac{3}{4}$ .

This engine’s own main skill is Multiplying Fractions. It practises find a fraction of a quantity alongside it.

Cutting the square into 3 rows and 4 columns makes $3 \times 4 = 12$ equal cells, and the two bands cross over $2 \times 3 = 6$ of them. That is the whole reason you multiply the tops and multiply the bottoms: the tops count the rows and columns the overlap covers, and the bottoms count the rows and columns the square was cut into. $\frac{6}{12}$ cancels by 6 to $\frac{1}{2}$ , the same rectangle regrouped into bigger pieces. Notice the overlap is smaller than either band on its own - taking a fraction OF something always shrinks it, which is why adding the two fractions can never be the answer.

Step 1. Build it. Slide the coral band to $\frac{2}{3}$ of the height and the teal band to $\frac{3}{4}$ of the width.
Step 2. Cancel it. The overlap covers 6 of the 12 cells. Pull the simplify handle as far as it will go.
Step 3. Without the square. The square is covered. What is $\frac{3}{5} \times \frac{2}{3}$ ?

What to say if they get stuck

$\frac{2}{3}$ of the HEIGHT and $\frac{3}{4}$ of the WIDTH. Drag one band at a time and watch the ruled cells change.
The whole square is now cut into $3 \times 4 = 12$ little cells, and the overlap covers $2 \times 3 = 6$ of them.
$\frac{6}{12}$ is not in its simplest form - both numbers divide by 6.

Open Area Grid on its own page to share it

How find a fraction of a quantity differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: calculate one unit or non-unit fraction of a quantity, and it stops where excludes chained operations.

Find a percentage of a quantity
Calculate one familiar percentage of a quantity. Excludes percentage change.
Multiply fractions
Multiply two proper fractions and simplify the result when required. Excludes finding a single fraction of a whole-number quantity.
Recognise equivalent fractions
Recognise two fractions representing the same value. Excludes arithmetic with non-equivalent fractions.

Related maths skills

All maths 11+ skills

Questions parents ask about find a fraction of a quantity

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

: Calculate one unit or non-unit fraction of a quantity. It is one of 55 named maths skills in the 11+, in the fractions, decimals and percentages strand, and this page carries 2 interactive exercises that practise it.
: One part of the bar is not the same as the shaded part. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Split 128 into 8 equal groups first, then take 3 of those groups - do not stop after one group.
: The skill map draws the line here: Excludes chained operations. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The fractions, decimals and percentages strand holds 9 skills that are tested together, and the pages next to find a fraction of a quantity are find a percentage of a quantity, identify a represented fraction and locate an equivalent value. Each has its own exercise and its own link, and none of them needs an account.
: Use Quantity Split and Area Grid, embedded on this page. They are the exercises the skill map attaches to find a fraction of a quantity, they run in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.

Start the free 11+ diagnostic