Writing, simplifying & ordering fractions – GCSE Maths

Foundation · Grade 1 · Non-calculator

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Two fractions are equivalent when they name the same amount of the whole. Multiply or divide the top and the bottom by the same number and the value does not change: $\frac{3}{5}=\frac{12}{20}$. Simplifying is the reverse — keep dividing until the top and bottom share no common factor other than $1$. $\frac{45}{60}=\frac{3}{4}$, not $\frac{9}{12}$, because you can still divide by $3$.

A mixed number $2\frac{3}{8}$ is two wholes and three eighths. Each whole is $\frac{8}{8}$, so $2\frac{3}{8}=\frac{16+3}{8}=\frac{19}{8}$. The other way, $\frac{17}{5}=3\frac{2}{5}$ because $17÷5=3$ remainder $2$.

To order fractions, give them a common denominator and compare numerators. Cross-multiplying $a\times d$ against $c\times b$ is a shortcut when you only have two fractions to compare.

Objectives

• Name the numerator and the denominator.
• Simplify a fraction by dividing top and bottom.
• Find a unit fraction of a whole number.

Key points

• Find equivalent fractions by multiplying or dividing top and bottom by the same number.
• Simplify a fraction fully by dividing by the highest common factor.
• Change a mixed number to an improper (top-heavy) fraction and back again.
• Order fractions by writing them with a common denominator.

Worked examples

Questions and answers

GCSE Maths writing, simplifying & ordering fractions questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Cancelling a number from the top only.

   Whatever you divide the top by, divide the bottom by as well.

2. Reading the denominator as the number you have.

   The bottom tells you the size of each part.

3. Thinking a larger denominator means a larger fraction.

   More equal parts means each part is smaller.

Exam tips

• Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Always give a fraction answer in its simplest form unless the question tells you otherwise — a final unsimplified fraction can lose the accuracy mark.
• In an ordering question, write each equivalent fraction clearly with the common denominator; that working is where the method marks are.

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

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Questions students ask

Related topics

• Addition & subtraction
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• BIDMAS
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• Factors & multiples
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• Metric conversions
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• Multiplication & division
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More on Writing, simplifying & ordering fractions

• Writing, simplifying & ordering fractions worked examples and method
  The method in order, key facts and the full lesson explanation

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.