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GCSE Maths / Edexcel

Simplifying and equivalent fractions

Simplify fractions by dividing the numerator and denominator by the same factor, and create equivalent fractions by multiplying both parts by the same number.

Number and Place ValueFoundation and HigherGrades 2 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Number > Fractions > Simplifying and equivalent fractions

Pearson Edexcel GCSE Maths number: use equivalent fractions and simplify fractions.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A fraction shows how many equal parts are being used. The top number is the numerator and the bottom number is the denominator.

Equivalent fractions have the same value even though they look different. For example, 1 / 2, 2 / 4, and 5 / 10 all mean the same amount.

To make an equivalent fraction, multiply or divide the numerator and denominator by the same number.

To simplify a fraction, divide the numerator and denominator by a common factor.

A fraction is fully simplified when the numerator and denominator have no common factor apart from 1.

For Foundation students, the safest method is to divide by a common factor you can see, then check if you can simplify again.

Key ruleWhatever you do to the numerator, do the same to the denominator.

Worked examples

Simplify once

Simplify 12 / 20.

  1. 12 and 20 are both divisible by 4.
  2. 12 / 4 = 3.
  3. 20 / 4 = 5.

Answer: 3 / 5

Simplify in steps

Simplify 18 / 30.

  1. 18 and 30 are both divisible by 2, giving 9 / 15.
  2. 9 and 15 are both divisible by 3.
  3. 9 / 3 = 3 and 15 / 3 = 5.

Answer: 3 / 5

Equivalent fraction

Write an equivalent fraction to 4 / 7 with denominator 28.

  1. The denominator changes from 7 to 28.
  2. 7 x 4 = 28.
  3. Multiply the numerator by 4 as well: 4 x 4 = 16.

Answer: 16 / 28

Common mistakes

  • Only dividing the numerator and not the denominator.
  • Adding the same number to the top and bottom instead of multiplying or dividing.
  • Stopping before the fraction is fully simplified.
  • Thinking a bigger numerator always means a bigger fraction.

Quick exercise

Try these before moving to the exam-style questions.

  1. Simplify 6 / 10.
  2. Simplify 15 / 25.
  3. Simplify 21 / 28.
  4. Complete the equivalent fraction: 2 / 3 = ? / 12.
  5. Complete the equivalent fraction: 5 / 8 = 20 / ?.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Simplify 24 / 36.

simplifying fractionsequivalent fractionsfoundation number
Standard exam styleFoundation and HigherNon-calculator3 marks

Complete the statement: 15 / 24 = ? / 8. Give the missing numerator.

equivalent fractionsmissing numeratorproportional reasoning
ChallengeFoundation and HigherNon-calculator3 marks

A student says 18 / 30 simplifies to 9 / 15, so the answer is finished. Explain the mistake and give the fully simplified fraction.

simplifying fractionserror analysiscommon factors