Solving linear equations with fractions
Use this guide to review fraction-based equations before trying your own problem in the app.
Start here if you want the short version before reading the full method.
- Fraction equations are often easiest once you clear the denominators first.
- Multiplying every term by the least common denominator usually reduces the clutter quickly.
What this topic means and what to look for first.
Fraction equations are often easier once you clear the denominators first.
Multiplying every term by the least common denominator can reduce clutter quickly.
One reliable route through the topic.
- 1Identify the least common denominator across the equation.
- 2Multiply every term by that denominator.
- 3Simplify the new equation.
- 4Solve the linear equation as usual.
- 5Check the answer in the original fraction equation.
See the method in action.
x/2 + 3 = 7
- Subtract 3 to get x/2 = 4.
- Multiply by 2.
- So x = 8.
x/3 + x/6 = 3
- Use 6 as the common denominator and multiply each term by 6.
- This gives 2x + x = 18.
- So 3x = 18 and x = 6.
Things that commonly send the method off track.
- Multiplying only one side of the equation by the common denominator.
- Making arithmetic slips when simplifying the cleared fractions.
Use a short verification pass before moving on.
- Substitute the answer into the original fraction equation rather than only the simplified line.
- Check that every denominator stayed non-zero after substitution.
Try a few variations before switching to a calculator or solver tool.
- x/4 + 2 = 6
- x/5 + x/10 = 3
- (x + 1)/3 = 4
Want to try a similar problem yourself?
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Extra algebra revision resources
If you want more printed algebra practice after this page, these broader searches are a sensible next step.
Amazon
Algebra workbook and revision book search
Useful if you want more equation, factorising, and worked-example practice in one printed source.
View Algebra workbook and revision book searchAmazon
GCSE algebra practice resources search
A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
View GCSE algebra practice resources searchNeed live help with fractions in equations?
Fraction steps are a common sticking point. Use the live-help route if you want help with the exact equation type or level.
What to include
- The topic or page you were reading
- The exam level or year group you care about
- Your country or timezone if live help timing matters
This is a live-help enquiry route, not an instant tutoring checkout. It helps CureMath understand demand and shape future partner or tutor options around real topics.
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Share the page with someone who is searching for the same maths topic before they go straight to a solver.
Short answers worth checking.
Not always, but it is usually the neatest and safest method for longer fraction equations.
Substitute your answer into the original fraction equation, not just the simplified one.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.