24 Fraction Questions And Answers To Test Fractions Knowledge And Skills From KS2 to GCSE

November 2, 2023 | 4 min read

Beki Christian

In this blog, we take a look at the sorts of skills pupils need to tackle fraction questions and fraction word problems, and then provide examples of the different sorts of fraction questions children are likely to encounter in KS2, KS3, and KS4.

Fractions key skills

Some of the key fractions skills that pupils will learn are:

How to find a fraction of an amount
How to add fractions and how to subtract fractions
Fraction, decimal, and percentage conversions

Below we will touch on each of these skills and provide links to more detail and examples.

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How to find a fraction of an amount

To find a fraction of a value, we need to know how to multiply fractions and how to divide fractions. The process involves dividing the value by the denominator and then multiplying that answer by the numerator.

For example, find $\cfrac{2}{5} \,$ of $30$

First, we find $\cfrac{1}{5} \,$ of $30,$ by dividing $30$ by $5.$

$\cfrac{1}{5} \,$ of $30 = 30 \div 5 = 6$

Next, we find $\cfrac{2}{5} \,$ of $30$ by multiplying the asnwer by $2.$

$\cfrac{2}{5} \,$ of $30 = 6 \times 2 = 12$

How to add or subtract fractions with different denominators

To add and subtract fractions with different denominators, we need to rewrite the fractions with a common denominator. To do this, we look for the lowest common multiple $(lcm)$ of the denominators.

Let’s look at an example: $\cfrac{2}{5} + \cfrac{1}{4}$

The $lcm$ of $5$ and $4$ is $20,$ so we rewrite the fractions, using our knowledge of equivalent fractions, with a denominator of $20.$

$fraction questions add subtract 1$ $fraction questions add subtract 2$

We can rewrite the first fraction as $\cfrac{8}{20} \,$ and the second fraction as $\cfrac{5}{20} \, .$

Therefore $\cfrac{2}{5} + \cfrac{1}{4}=\cfrac{8}{20}+\cfrac{5}{20}$

Once we have the two fractions written with the same denominator, we can add the numerators. The denominator remains the same.

$\cfrac{8}{20}+\cfrac{5}{20}=\cfrac{13}{20}$

How to compare and convert fractions, decimals and percentages

Fractions are one way of measuring parts of a whole. Percentages and decimals are other ways of measuring parts of a whole. Pupils will first learn about key equivalences between the most common fractions, decimals and percentages, such as halves, quarters, and tenths. Later, in KS3, they will then learn methods for converting between any fractions, decimals, and percentages.

Here are some helpful visuals for the most common fractions, decimals, and percentages:

Fraction questions

There are a variety of fraction questions that might be asked in KS2, KS3, and KS4. Here we focus on fraction word problems and problem-solving questions which often provide the greatest challenge to pupils at primary school and secondary school.

At KS2, using real-world problems together with concrete resources or maths manipulatives is one of the best ways to help pupils visualise and understand what they are being asked to do.

In KS3 and KS4, word problems and problem solving questions can encourage students to think more deeply about about the processes and steps involved in a question.

Fractions in KS2

At the beginning of KS2, pupils will have an understanding of basic fractions, such as $\cfrac{1}{2}, \cfrac{1}{4},$ and $\cfrac{3}{4}.$

They will be able to write a fraction and find a fraction of a shape or a quantity. Over the course of KS2, they will spend a significant amount of time developing their knowledge of fractions. By the end of KS2, pupils will have covered:

Finding a fraction of a quantity
Equivalent fractions
Ordering and comparing fractions
Adding and subtracting fractions with the same denominator
Adding and subtracting fractions with different denominators
Multiplying fractions and dividing fractions by whole numbers and fractions
Improper fractions and mixed numbers (sometimes called mixed fractions)
Equivalences between fractions, decimal and percentages

Find out more: KS2 fractions: a teacher’s guide

A Third Space Learning online Year 5 lesson using equivalent fraction questions. — A Third Space Learning online Year 5 lesson on equivalent fractions.

Lower KS2 fraction questions

4

10

5

2

$\cfrac{1}{4} \,$ of $20 = 20 \div 4 = 5$

\cfrac{2}{5}

\cfrac{3}{5}

\cfrac{1}{5}

\cfrac{3}{10}

He gave away $\cfrac{1}{5}+\cfrac{2}{5}=\cfrac{3}{5}$

\cfrac{4}{5}

\cfrac{2}{5}

\cfrac{2}{4}

\cfrac{10}{4}

$fraction questions lower KS2 2$

Upper KS2 fraction questions

20

18

4

12

$\cfrac{1}{8} \,$ of $32 = 32 \div 8 = 4$

$\cfrac{3}{8} \,$ of $32 = 4 \times 3=12,$ so there are $12$ girls.

$32-12=20,$ so there are $20$ boys.

\cfrac{2}{3}

\cfrac{20}{30}

\cfrac{24}{36}

\cfrac{12}{13}

$fraction questions upper KS2 1$ $fraction questions upper KS2 2$

$\cfrac{12}{13} \,$ is not equivalent to $\cfrac{2}{3} \,$ so it is the odd one out.

=

<

>

$fraction questions upper KS2 4$

Therefore $\cfrac{3}{4} > \cfrac{13}{20}$

\cfrac{7}{15}

\cfrac{1}{2}

\cfrac{13}{15}

\cfrac{3}{8}

$\cfrac{2}{3}-\cfrac{1}{5} = \cfrac{10}{15}-\cfrac{3}{15} =\cfrac{7}{15}$

\cfrac{15}{35}

\cfrac{3}{35}

2\cfrac{1}{7}

5\cfrac{3}{7}

$5 \times \cfrac{3}{7} = \cfrac{15}{7} = 2 \cfrac{1}{7}$

$fraction questions upper KS2 5$

60

30

4.8

48

$\begin{aligned} \cfrac{2}{5}&=12\\\\ \cfrac{1}{5}&=12 \div 2 = 6\\\\ \cfrac{5}{5}&=6 \times 5 = 30 \end{aligned}$

Looking for more KS2 fraction questions?

These fraction worksheets provide lots more fraction questions, covering both basic elements and more complex problems. Answers are also included:

Fractions in KS3

In KS3, pupils develop their confidence in working with fractions. They practise all of the skills learnt at KS2 and learn to apply these to a variety of problems. Fractions will be learnt about as a topic in their own right, but will also be increasingly embedded into other areas of maths, such as algebra and geometry, as pupils progress through KS3.

Manipulating fractions questions

\cfrac{3}{5}

\cfrac{2}{5}

\cfrac{3}{8}

\cfrac{5}{8}

For every $3$ men, there are $5$ women. Therefore in a total of $8$ people, there are $3$ men. The fraction of the workers who are men is $\cfrac{3}{8} \, .$

Yes

We can’t tell

$2 \cfrac{1}{3} \,= \cfrac{2 \times 3 +1}{3} \, = \cfrac{7}{3}$

$\cfrac{7}{3} = \cfrac{14}{6}$

Finding a fraction of an amount questions

800

1500

1400

500

$\cfrac{3}{8} \,$ of $2400$

$2400 \div 8 =300$

$300 \times 3=900$

$\cfrac{5}{12} \,$ of $2400$

$2400 \div 12 =200$

$200 \times 5=1000$

$2400-900-1000=500$

£252000

£308000

£28000

£277200

$\cfrac{1}{10} \,$ of $280000$

$280000 \div 10=28000$

$280000-28000=252000$

Calculating with fractions and mixed numbers questions

\cfrac{5}{8} \div \cfrac{4}{5}=\cfrac{5}{8} \times \cfrac{4}{5} =\cfrac{20}{40}

\cfrac{5}{8} \div \cfrac{4}{5}=\cfrac{25}{40} \div \cfrac{32}{40} =\cfrac{0.78125}{40}

\cfrac{5}{8} \div \cfrac{4}{5}=\cfrac{8}{5} \times \cfrac{4}{5} =\cfrac{32}{40}

\cfrac{5}{8} \div \cfrac{4}{5}=\cfrac{5}{8} \times \cfrac{5}{4} =\cfrac{25}{32}

4\cfrac{3}{7} \; \mathrm{km}

4\cfrac{11}{12} \; \mathrm{km}

2\cfrac{5}{12} \; \mathrm{km}

1\cfrac{7}{12} \; \mathrm{km}

$\begin{aligned} 1\cfrac{1}{4} + 3\cfrac{2}{3} &= \cfrac{5}{4}+\cfrac{11}{3}\\\\ &= \cfrac{15}{12} +\frac{44}{12}\\\\ &=\cfrac{59}{12}\\\\ &=4\cfrac{11}{12} \end{aligned}$

Fractions, decimals and percentages questions

32\%

40\%

80\%

60\%

$\cfrac{32}{40}=\cfrac{8}{10}=80\%$

\cfrac{47}{20}

\cfrac{235}{100}

2 \cfrac{7}{20}

2 \cfrac{35}{100}

$2.35= \cfrac{235}{100}$

Simplifying $\cfrac{235}{100}$ gives us $\cfrac{47}{20}$

Ensure you follow the instructions carefully and give your answer as an improper
fraction in its simplest form.

Fractions in KS4 and for GCSE

In KS4, students continue to develop their fluency in using fractions to solve problems and will be required to apply their knowledge of fractions within many different maths topics. GCSE maths papers, from all exam boards (including AQA, Edexcel and OCR) will, almost certainly, contain questions involving fractions.

These may appear as standard procedural questions, such as calculate $2\cfrac{1}{4} \times 3\cfrac{2}{3} \,.$ It is also likely that there will be questions from other areas of maths, such as algebra, geometry, and probability, which involve fractions.

Take a look at our GCSE maths guides on fractions:

GCSE fraction questions (Foundation)

\cfrac{3}{10} \, , \cfrac{3}{8} \, , \cfrac{9}{20} \, , \cfrac{2}{5}

\cfrac{3}{10} \, , \cfrac{2}{5} \, , \cfrac{3}{8} \, , \cfrac{9}{20}

\cfrac{3}{8}\, , \cfrac{2}{5} \, , \cfrac{3}{10} \, , \cfrac{9}{20}

\cfrac{3}{10} \, , \cfrac{3}{8} \, , \cfrac{2}{5} \, , \cfrac{9}{20}

$\cfrac{2}{5} \, =\cfrac{16}{40}$

$\cfrac{3}{8} \, =\cfrac{15}{40}$

$\cfrac{3}{10} \, =\cfrac{12}{40}$

$\cfrac{9}{20} \, =\cfrac{18}{40}$

$\cfrac{12}{40}, \, \cfrac{15}{40} , \, \cfrac{16}{40}, \, \cfrac{18}{40}$

$\cfrac{3}{10}, \, \cfrac{3}{8} , \, \cfrac{2}{5}, \, \cfrac{9}{20}$

3\cfrac{5}{12}

1\cfrac{17}{24}

2\cfrac{8}{11}

1\cfrac{4}{11}

$\begin{aligned} 1 \cfrac{1}{3} \, + 1 \cfrac{1}{3} \, + \cfrac{3}{8} \, + \cfrac{3}{8} &= \cfrac{4}{3} + \cfrac{4}{3} \, + \cfrac{3}{8} \, +\cfrac{3}{8}\\\\ &=\cfrac{32}{24} \, + \cfrac{32}{24} \, + \cfrac{9}{24} \, +\cfrac{9}{24}\\\\ &=\cfrac{82}{24}\\\\ &= \cfrac{41}{12}\\\\ &=3 \cfrac{5}{12} \end{aligned}$

\cfrac{2}{3}

\cfrac{16}{81}

\cfrac{32}{243}

\cfrac{64}{729}

$\cfrac{8}{27} \, \times \cfrac{2}{3} = \cfrac{16}{81}$

$\cfrac{16}{81} \, \times \cfrac{2}{3} = \cfrac{32}{243}$

GCSE fraction questions (Higher)

300

240

280

320

$\cfrac{3}{4} \,$ of the sheep are white. $\cfrac{2}{3} \, \times \cfrac{3}{4} \, = \cfrac{6}{12} \,$ of the sheep are white ewes.

$\cfrac{1}{4} \,$ of the sheep are black. $\cfrac{2}{5} \, \times \cfrac{1}{4} \, = \cfrac{2}{20} \,$ of the sheep are black ewes.

$\cfrac{6}{12} \, +\cfrac{2}{20} \, =\cfrac{30}{60} \, +\cfrac{6}{60} \, =\cfrac{36}{60}$

$\cfrac{36}{60} \,$ of the sheep are ewes.

$\cfrac{36}{60}=144$

$\cfrac{1}{60} \, =144 \div 36=4$

$\cfrac{60}{60} \, = 4 \times 60=240$

\cfrac{-2x+2}{(x+4)(x-2)}

\cfrac{-2x+22}{(x+4)(x-2)}

\cfrac{-2}{(x+4)(x-2)}

\cfrac{-2x-2}{(x+4)(x-2)}

$\begin{aligned} \cfrac{3}{x-2}\,-\cfrac{5}{x+4} \, &=\cfrac{3(x+4)}{(x+4)(x-2)}\,-\cfrac{5(x-2)}{(x+4)(x-2)}\\\\ &=\cfrac{3x+12-(5x-10)}{(x+4)(x-2)}\\\\ &=\cfrac{-2x+2}{(x+4)(x-2)} \end{aligned}$

\cfrac{-9}{128}

\cfrac{9}{4}

\cfrac{-9}{4}

\cfrac{-9}{8}

$\begin{aligned} \cfrac{ab^{2}}{c} \, &=\cfrac{-2 \times (\cfrac{3}{8})^{2}}{\cfrac{1}{4}}\\\\ &=\cfrac{-2 \times \cfrac{9}{64}}{\cfrac{1}{4}}\\\\ &=\cfrac{-\cfrac{18}{64}}{\cfrac{1}{4}}\\\\ &=-\cfrac{18}{64} \, \times \cfrac{4}{1}\\\\ &=-\cfrac{72}{64}\\\\ &=-\cfrac{9}{8} \end{aligned}$

\cfrac{281}{990}

\cfrac{31}{110}

\cfrac{281}{1000}

\cfrac{281}{999}

$\begin{aligned} x&=0.281818181…\\\\ 10x&=2.81818181…\\\\ 1000x&=281.818181…\\\\ 990x&=279\\\\ x&=\cfrac{279}{990}\\\\ x&=\cfrac{31}{110} \end{aligned}$

Looking for more KS3 and KS4 fraction questions?

These GCSE maths worksheets provide lots more fraction questions with answers included:

More GCSE fraction support

Third Space Learning’s free GCSE maths resource library contains detailed lessons with step-by-step instructions on how to solve fraction problems at secondary, as well as fraction worksheets with practice questions and more GCSE exam questions.

Fraction questions FAQs

What is a fraction of an amount at GCSE?

A fraction of an amount at GCSE is when we are asked to find a certain fraction of an amount, for example $\cfrac{3}{5} \,$ of $20.$

To do this, we divide by the denominator and then multiply by the numerator.

$20\div 5 = 4$

$4 \times 3 =12$

So $\cfrac{3}{5}$ of $20=12.$

What is an example of a fraction?

An example of a fraction is $\cfrac{3}{10}.$ This is read as ‘three tenths’ and means thee out of every ten.

You may see different types of fractions:

Unit fractions have a numerator of $1,$ for example $\cfrac{1}{8} \, .$

Proper fractions have a numerator that is smaller than the denominator, for example $\cfrac{3}{4} \, .$

Improper fractions have a numerator that is greater than the denominator, for example $\cfrac{5}{2} \, .$

Mixed number fractions (mixed fractions) are made up of a whole number and a fraction, for example $2\cfrac{1}{3} \, .$

How to simplify fractions

When pupils learn how to simplify fractions we look for common factors of the numerator and the denominator. If there are common factors, we divide both the numerator and the denominator by the common factor to find an equivalent, simpler fraction. We continue doing this until there are no more common factors.
For example, simplify $\cfrac{20}{40} \, .$
$10$ is a common factor of $20$ and $40.$ Dividing both $20$ and $40$ by $10$ gives us $\cfrac{2}{4} \, .$
$2$ is a common factor of $2$ and $4.$ Dividing both $2$ and $4$ by $2$ gives us $\cfrac{1}{2} \, .$

There are no more common factors of $1$ and $2,$ so we cannot simplify any further.

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