Number
№ 124Sheet № 124 · Foundation + Higher · AQA · Edexcel · OCR
Equivalent Fractions and Simplifying –
Equivalent fractions and simplifying are essential skills that underpin almost every fractions question on GCSE Maths papers. You need to recognise when two fractions represent the same value and reduce fractions to their simplest form quickly and accurately.
§Key definitions
Question:
Simplify 18/24.
Answer:
7/11 is larger.
Q1 (Foundation):
Simplify 15/25.
Q2 (Foundation):
Write three fractions equivalent to 3/7.
Q3 (Higher):
Which is larger, 9/13 or 11/16? Show your working.
§Formulas to memorise
To simplify a/b, divide both a and b by HCF(a, b)
To compare a/b and c/d by cross-multiplying: if ad > bc then a/b > c/d
Worked example
Simplify 18/24.
Working:
⚠ Common mistakes
- ✗Dividing by a common factor that is not the HCF. For example, simplifying 24/36 by dividing by 2 to get 12/18, then stopping. Always check if you can simplify further, or find the HCF first.
- ✗Multiplying numerator and denominator by different numbers. Both must be multiplied or divided by the same value to keep the fraction equivalent.
- ✗Confusing cross-multiplication direction. When comparing a/b and c/d, compute ad and bc. If ad > bc then a/b is larger.
✦ Exam tips
- →Always give your final answer in its simplest form unless told otherwise.
- →If the numbers are large, use prime factorisation to find the HCF efficiently.
- →When comparing fractions on a non-calculator paper, cross-multiplication is faster than finding a common denominator.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/equivalent-fractions-and-simplifying