GCSE MATHS • HIGHER TIER
Equations with Fractions Made Simple
Learn how to clear denominators, use the lowest common multiple, solve fraction equations and check your answers accurately.
Clear method
Exam practice
Worked proofs
Equations with Fractions in Four Moves
1
Identify
Identify the denominator or denominators in the equation.
2
Clear
Multiply both sides by the denominator or lowest common multiple.
3
Solve
Simplify and solve using normal equation methods.
4
Check
Substitute the answer into the original equation.
What You’ll Learn
Understand Fraction Equations
Recognise equations containing one or more fractions with a variable.
Clear Denominators
Multiply both sides by the correct denominator.
Use the LCM
Use the lowest common multiple when several denominators are present.
Solve Bracket Fractions
Remove the denominator before simplifying bracket expressions.
Check Solutions
Substitute answers into the original equation.
Key Rules
What Are Equations with Fractions?
Equations with fractions contain one or more fractions involving a variable. The goal is still the same: find the value of the unknown variable.
Multiply both sides by 4:
x/4 = 5
x = 20
Why Are Equations with Fractions Important?
Fraction equations develop algebraic fluency and combine fraction skills with equation-solving techniques.
The Golden Rule
To remove fractions, multiply both sides of the equation by the denominator. This helps eliminate fractions and simplifies the equation.
Worked Proof: Equations with Fractions
Step-by-Step Method
- 1. Identify the denominator.
- 2. Multiply both sides by the denominator.
- 3. Simplify the equation.
- 4. Solve using normal equation methods.
- 5. Check your answer.
More Worked Examples
1
Solve x/3 = 7
Multiply both sides by 3
x = 21
2
Solve x/5 + 2 = 8
Subtract 2 :
x/5 = 6
Multiply by 5 :
Multiply by 5 :
3
Solve (x + 4)/2 = 9
Multiply both sides by 2 :
x + 4 = 18
Subtract 4 :
Subtract 4 :
4
Solve (2x - 3)/4 = 5
Multiply both sides by 4 :
2x - 3 = 20
Add 3 :
2x = 23
Divide by 2 :
Add 3 :
2x = 23
Divide by 2 :
- Common GCSE Mistakes
- Both sides: Multiply the whole equation, not just one side.
- Wrong denominator: Use the correct denominator or LCM.
- Arithmetic errors: Simplify each step carefully.
- Unsimplified fractions: Reduce fractions where needed.
- No check: Substitute the answer back into the original equation.
- Exam Tips
- Clear fractions first: Remove denominators before solving.
- Use the LCM: Clear several denominators in one step.
- Multiply every term: Apply the multiplier to the whole equation.
- Show each step: Keep the working clear and organised.
- Check by substitution: Confirm the solution works.
Skills Used in Equations with Fractions
One-Step Equations
Two-Step Equations
Equations with Brackets
Algebraic Fractions
Rearranging Formulae
Simultaneous Equations
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Equations with Fractions Tutorial
Step-by-step walkthroughs of Equations with Fractions with clear methods and exam tips.
Frequently Asked Questions
Identify the denominator and multiply both sides by it to clear the fraction.
Use the lowest common multiple of the denominators to clear all fractions.
Yes. Multiply every term on both sides of the equation.
Clear the denominator first, then simplify the bracket expression and solve.
Substitute your solution into the original fraction equation.
They link closely to one-step equations, two-step equations, equations with brackets, algebraic fractions and simultaneous equations.
