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Free GCSE maths resource

GCSE fractions practice and starter worksheets

Practise reading fractions, finding fractions of amounts and calculating with fractions. Learn from worked examples, then try a short practice set.

Foundation and Higher · Useful for students strengthening core skills before mixed GCSE practice.

Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.

Higher extension. No questions in this selected set are labelled Higher extension. These core methods also support Higher revision.

4 worked examples and 8 original practice questions · Allow 35–50 minutes · Read online or print. Higher extensions are labelled. No account or email needed.

Learn the methodTry the questions

Printing includes the method, examples and space for working, followed by a separate answer section.

A useful approach

  1. Check that a shape is split into equal parts before writing a fraction of it.
  2. For a fraction of an amount, divide by the denominator and multiply by the numerator.
  3. For addition or subtraction, use a common denominator. For multiplication, multiply the numerators and denominators, then simplify.

A mistake to watch for

Adding denominators changes the size of the parts. First express both fractions using the same-sized parts.

Learn each method, then practise it

Read each line of working and explain why it follows from the previous line.

Equivalent fractions and simplifying

Divide numerator and denominator by the same common factor. This changes how the fraction is written, not its value.

Worked example 1

Writing, Simplifying and Ordering Fractions · Core GCSE skill · Calculator allowed · 1 marks

Write the fraction in its simplest form.

  1. The highest common factor of 12 and 18 is 6.
  2. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so = .
  3. Dividing numerator and denominator by the same non-zero number preserves the fraction’s value. Using the highest common factor leaves no further whole-number factor to cancel.
Answer:
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Now practise this method: Question 1 · Question 2

A fraction of an amount

Divide by the denominator to find one equal part, then multiply by the numerator. If asked what remains, subtract the fraction amount from the whole.

Worked example 2

Fractions of an Amount · Core GCSE skill · Calculator allowed · 1 marks

Work out of 92

  1. 92 ÷ 4 = 23.
  2. 23 × 3 = 69.
Answer: 69
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Now practise this method: Question 3 · Question 4

Adding and subtracting fractions

Use a common denominator so the pieces have the same size. Add or subtract the numerators, keeping that denominator, then simplify. Convert mixed numbers to improper fractions first.

Worked example 3

Fractions · Core GCSE skill · No calculator · 3 marks

  1. One of these fractions is not equivalent to

            

    Write down this fraction.

  2. Work out +
  1. a) , and all simplify to , but does not ( = , not ).
  2. b) Use denominator 15: = and = .
  3. + = .
Answer: (a)   (b)
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Now practise this method: Question 5 · Question 6 · Question 8

Multiplying fractions

Multiply the numerators and multiply the denominators, then cancel common factors. A common denominator is not needed for multiplication.

Worked example 4

Fractions · Core GCSE skill · No calculator · 2 marks

Work out ×

Give your answer as a fraction in its simplest form.

  1. Multiply the numerators and multiply the denominators: 4 x 3 = 12 and 9 x 10 = 90, so the product is .
  2. Divide top and bottom by 6: = .
Answer:
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Now practise this method: Question 7 · Question 8 · Question 6

Your practice questions

Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.

Question 2

Writing, Simplifying and Ordering Fractions · Core GCSE skill · Calculator allowed · 2 marks

The grid is made of 12 equal squares.

8 of the squares are shaded.

Write the fraction of the grid that is shaded. Give your fraction in its simplest form.

Diagram for Writing, Simplifying and Ordering Fractions. The question states the required measurements and relationships.
Read a text description of this diagram

Given diagram. The grid is made of 12 equal squares. 8 of the squares are shaded. Write the fraction of the grid that is shaded. Give your fraction in its simplest form. Use the labelled information; do not estimate measurements from the sketch.

Check answer and working for question 2

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Worked answers: Fractions

Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.

Answer 1

Show answer and working for question 1
  1. = , = and = .
  2. simplifies to , so is not equivalent to .
Answer:
Back to question 1

Answer 2

Show answer and working for question 2
  1. 8 out of 12 squares are shaded, giving .
  2. Divide top and bottom by 4: = .
Answer:
Back to question 2

Answer 4

Show answer and working for question 4
  1. £64 ÷ 8 = £8, so of £64 = 3 × £8 = £24.
  2. Money left = £64 − £24 = £40.
Answer: £40
Back to question 4

Answer 5

Show answer and working for question 5
  1. Write as improper fractions: 4 = and 1 = .
  2. Use denominator 20: = and = .
  3. - = = 2.
Answer: 2
Back to question 5

Answer 6

Show answer and working for question 6
  1. a) 1 = and 2 = . Using denominator 12: = and = .
  2. a) + = = 4.
  3. b) 2 = and 1 = , so x = = 3.
Answer: (a) 4   (b) 3
Back to question 6

Answer 7

Show answer and working for question 7
  1. Write both numbers as improper fractions: 2 = and 1 = .
  2. Multiply: x = .
  3. Simplify: = 5, as required. (Or cancel the 8s first: = 5.)
Answer: 2 = and 1 = , so the product is = = 5
Back to question 7

Answer 8

Show answer and working for question 8
  1. a) Use denominator 40: = and = .
  2. a) - = .
  3. b) Write as improper fractions: 1 = and 2 = .
  4. b) x = = = 3, as required.
Answer: (a)   (b) x = = = 3
Back to question 8

Practise a specific skill

Workouts provide interactive practice; choose the tier your school has recommended.

Use this in class

Use the first question to discuss equal parts, then ask pupils to explain their chosen operation before calculating. Leave time to simplify each final fraction.

Build a custom classroom worksheet or print this page. The teacher builder can display questions on a projector and reveal answers separately.

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