GCSE MATHS • HIGHER TIER
Solving Algebraic Fractions Made Simple
Learn how to remove fractions from algebraic equations, keep equations balanced, solve for unknown values and check your solutions accurately.
Clear method
Exam practice
Worked proofs
Proof in Four Moves
1
Identify
Find the denominator or denominators.
2
Multiply
Multiply both sides by the denominator or the LCM.
3
Simplify
Remove the fractions and simplify the equation.
4
Solve
Use standard equation methods to isolate the variable.
5
Check
Substitute the answer into the original equation.
What You’ll Learn
Clear denominators
Remove fractions by multiplying both sides of an equation by the denominator.
Keep equations balanced
Apply the same operation to both sides so the equation remains valid.
Solve algebraically
Simplify and isolate the variable using standard equation-solving methods.
Check solutions
Substitute your answer back into the original equation to confirm it is correct.
Key Rules
Multiply both sides
Use the LCM when needed
Multiply every term
Solve after clearing fractions
Worked Proof: Consecutive Numbers
1. Identify
Identify the denominator: 5.
2. Multiply
Multiply both sides by 5: x + 2 = 20.
3. Simplify
Simplify the equation.
4. Subtract
Subtract 2 from both sides: x = 18.
5. Check
Check by substituting x = 18 into the original equation.
More Worked Examples
1
Simple denominator
Solve x / 4 = 5.
x = 20.
2
Another one-step equation
Solve x / 6 = 3.
x = 18.
3
Coefficient in the numerator
Solve 2x / 3 = 8.
Divide both sides by 2: x = 12.
4
Subtraction in the numerator
Solve (x - 4) / 7 = 2.
Add 4: x = 18.
5
Multi-step numerator
Solve (3x + 1) / 4 = 7.
Subtract 1: 3x = 27.
Divide by 3: x = 9.
6
Fraction plus a constant
Solve x / 2 + 3 = 8.
Multiply by 2: x = 10.
- Common GCSE Mistakes
- Forgetting to multiply every term when clearing fractions.
- Trying to solve before removing the fraction.
- Applying an operation to only one side of the equation.
- Making sign mistakes when adding or subtracting.
- Arithmetic errors after the denominator has been removed.
- Exam Tips
- Identify all denominators before you start.
- Use the LCM when several denominators are present.
- Show every algebraic step clearly.
- Keep the equation balanced at every stage.
- Check the final answer by substitution
Skills Used in Algebraic Proof
Ready to Practise?
Printable Worksheet
Practise algebraic fraction equations and review answers step by step.
Interactive Quiz
Test denominator clearing, equation solving and checking solutions with instant feedback.
Exam-Style Questions
Use timed Higher Tier-style questions to build confidence for the real exam.
Watch the Solving Algebraic Fractions Tutorial
Follow step-by-step walkthroughs showing how to clear denominators, keep equations balanced, solve multi-step algebraic fraction equations and check solutions.
Frequently Asked Questions
It is an equation where one or more fractions contain algebraic terms, such as x/3 = 4 or (x + 2)/5 = 3.
Multiply both sides by the denominator to eliminate the fraction, then solve the resulting equation normally.
Multiply every term by the lowest common multiple of the denominators so all fractions are removed simultaneously.
Doing the same operation to both sides keeps the equation balanced and preserves its equality.
Substitute the value you found back into the original equation and check that both sides are equal.
