Sheet № 138 · Foundation + Higher · AQA · Edexcel · OCR
Solving Equations with Fractions –
Equations with fractions appear on both Foundation and Higher papers and are a common source of lost marks. The key idea is simple: clear the fractions first by multiplying every term by the lowest common denominator (LCD). Once the fractions are gone, you solve the equation using the techniques you already know. This page teaches you the
§Key definitions
Question:
Solve x/3 + 2 = 5.
Answer:
No solution
Q1 (Foundation):
Solve x/5 + 3 = 7.
Q2 (Foundation):
Solve (x + 4)/2 = 6.
Q3 (Higher):
Solve (3x − 1)/4 + (x + 2)/6 = 2.
§Formulas to memorise
To clear fractions, multiply every term by the lowest common denominator (LCD)
Cross-multiplication: if a/b = c/d then ad = bc
Identify every denominator — in the equation.
Find the LCD — of all denominators.
Multiply every term on both sides — by the LCD. This eliminates all fractions.
Expand any brackets — that result from the multiplication.
Solve the resulting equation — using standard methods (collect terms, isolate x).
Check your answer — by substituting back into the original equation.
Worked example
Solve x/3 + 2 = 5.
Working:
⚠ Common mistakes
- ✗Forgetting to multiply every term by the LCD. Students often multiply the fractions but forget to multiply whole-number terms on the other side. Every term must be multiplied.
- ✗Sign errors when expanding brackets. Watch out for minus signs before brackets, such as −3(x − 2) = −3x + 6, not −3x − 6.
- ✗Using cross-multiplication when there are more than two fractions. Cross-multiplication only works when you have one fraction equal to another fraction. Use the LCD method for anything more complex.
✦ Exam tips
- →Always show the LCD multiplication step clearly — examiners award method marks for this.
- →If a question says "solve algebraically," you must show working, not trial-and-improvement.
- →Substitute your answer back in to check, especially when there are multiple fractions.
- →On Higher papers, you may get x in the denominator. Multiply through carefully and note any values that make the denominator zero (these are excluded).