Which fraction is equivalent to 7/11?

28/44. Multiplying the top and the bottom of 7/11 by 4 gives 28/44, which means the same amount of the bar is shaded even though there are 4 times as many pieces.

What does a child have to do to recognise equivalent fractions in the 11+?

Recognise two fractions representing the same value. It is one of 55 named maths skills in the 11+, in the fractions, decimals and percentages strand, and this page carries 3 interactive exercises that practise it.

What is the trap in an 11+ recognise equivalent fractions question?

Adding the same number to the top and the bottom does not keep the fraction the same. 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 recognise equivalent fractions?

Point at the next move rather than explaining the whole rule. Multiply the top and the bottom of 7/11 by the same number - both parts have to grow together.

What does recognise equivalent fractions lead on to?

Once it is secure, the skill map opens convert fraction and decimal. Equivalent partitioning supports familiar fraction and decimal conversion.

What is not part of recognise equivalent fractions in the 11+?

The skill map draws the line here: Excludes arithmetic with non-equivalent fractions. 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 recognise equivalent fractions?

The fractions, decimals and percentages strand holds 9 skills that are tested together, and the pages next to recognise equivalent fractions are convert decimal and percentage, convert fraction and decimal and convert fraction and percentage. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise recognise equivalent fractions for free?

Use Fraction Slicer, Area Grid and Quantity Split, embedded on this page. They are the exercises the skill map attaches to recognise equivalent fractions, 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

Recognise equivalent fractions

Recognise two fractions representing the same value.

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

Slice the chocolate bar into 4 equal pieces, then shade 3 of them.

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.

Equivalent fractions for $\frac{7}{11}$

Which fraction is equivalent to $\frac{7}{11}$ ?

Splitting each of the 11 parts into 4 gives 44 smaller parts, and 28 of them are shaded.

A bar cut into 11 equal parts, with 7 of them shaded.

$\frac{40}{44}$
$\frac{27}{44}$
$\frac{28}{11}$
$\frac{28}{44}$

Answer: $\frac{28}{44}$

How you get there

Multiplying the top and the bottom of $\frac{7}{11}$ by 4 gives $\frac{28}{44}$ , which means the same amount of the bar is shaded even though there are 4 times as many pieces.

Why the other answers tempt

Adding the same number to the top and the bottom does not keep the fraction the same.

If they are stuck, say this

Multiply the top and the bottom of $\frac{7}{11}$ by the same number - both parts have to grow together.

Now do it live in Fraction Slicer

How each of these 3 exercises teaches it

Fraction Slicer

Slice the chocolate bar into 4 equal pieces, then shade 3 of them.

Cutting every piece again multiplies how many pieces there are AND how many you shade, so the amount of chocolate never changes. $\frac{3}{4}$ , $\frac{6}{8}$ and $\frac{9}{12}$ are one single quantity wearing three different numbers. That is what "equivalent" means: different names, identical amount.

Step 1. Slice & shade. Slice the bar into equal pieces, then tap pieces to shade three quarters of it.
Step 2. The overlay. Lower the teal bar onto yours. Where does each shading stop?

What to say if they get stuck

Drag the CUTS slider until the bar falls into 4 equal pieces.
The bottom number says how many pieces the WHOLE is cut into. The top number says how many of them you take.
In step 2, lower the teal bar straight down onto yours and watch where each shading STOPS.

Open Fraction Slicer 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 recognise equivalent fractions 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

Quantity Split

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

This engine’s own main skill is Finding a Percentage of a Quantity. It practises recognise equivalent fractions alongside 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

Where recognise equivalent fractions sits in the 11+

The 11+ does not test these skills in isolation, and practising one in the wrong order wastes the practice. These are the skills the curriculum map connects this one to.

This opens up: Convert fraction and decimal
Equivalent partitioning supports familiar fraction and decimal conversion.

How recognise equivalent fractions 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: recognise two fractions representing the same value, and it stops where excludes arithmetic with non-equivalent fractions.

Find a fraction of a quantity
Calculate one unit or non-unit fraction of a quantity. Excludes chained operations.
Find a percentage of a quantity
Calculate one familiar percentage of a quantity. Excludes percentage change.
Identify a represented fraction
Name the fraction represented by equal parts. Parts must form one equal-part whole.
Multiply fractions
Multiply two proper fractions and simplify the result when required. Excludes finding a single fraction of a whole-number quantity.

Related maths skills

All maths 11+ skills

Questions parents ask about recognise equivalent fractions

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.

: Recognise two fractions representing the same value. It is one of 55 named maths skills in the 11+, in the fractions, decimals and percentages strand, and this page carries 3 interactive exercises that practise it.
: Adding the same number to the top and the bottom does not keep the fraction the same. 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. Multiply the top and the bottom of $\frac{7}{11}$ by the same number - both parts have to grow together.
: Once it is secure, the skill map opens convert fraction and decimal. Equivalent partitioning supports familiar fraction and decimal conversion.
: The skill map draws the line here: Excludes arithmetic with non-equivalent fractions. 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 recognise equivalent fractions are convert decimal and percentage, convert fraction and decimal and convert fraction and percentage. Each has its own exercise and its own link, and none of them needs an account.
: Use Fraction Slicer, Area Grid and Quantity Split, embedded on this page. They are the exercises the skill map attaches to recognise equivalent fractions, 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.

Recognise equivalent fractions is the step before convert fraction and decimal

A free diagnostic maps the whole run of skills either side of this one, so practice follows the order the paper actually needs.

Start the free 11+ diagnostic