Sheet № 75 · Foundation + Higher · AQA · Edexcel · OCR
Multiplying and Dividing Fractions –
Multiplying and dividing fractions appears on every GCSE Maths paper across AQA, Edexcel, and OCR. Once you know the two core rules — multiply straight across, and Keep-Change-Flip for division — these questions become some of the easiest marks on the exam.
§Key definitions
Dividing fractions
uses the reciprocal. Instead of dividing by a fraction, you multiply by its reciprocal (the fraction flipped upside down). This is often remembered as Keep-Change-Flip: keep the first fraction, change ÷ to ×, flip the second fraction.
Question:
Work out 3/4 × 2/5. Give your answer as a fraction in its simplest form.
Q1 (Foundation):
Work out 5/8 × 4/9. Give your answer in its simplest form.
Q2 (Foundation):
Work out 3/5 ÷ 2/3.
Q3 (Higher):
Work out 1 2/5 × 2 1/3. Give your answer as a mixed number in its simplest form.
§Formulas to memorise
a/b × c/d = ac / bd — multiply numerators together and denominators together
a/b ÷ c/d = a/b × d/c = ad / bc — Keep-Change-Flip, then multiply
The reciprocal of a/b is b/a — flipping a fraction gives its reciprocal
Worked example
Work out 3/4 × 2/5. Give your answer as a fraction in its simplest form.
Working:
⚠ Common mistakes
- ✗Finding a common denominator when multiplying. You do not need a common denominator for multiplication — just multiply straight across.
- ✗Flipping the wrong fraction when dividing. Only flip the second fraction (the divisor). Keep the first fraction exactly as it is.
- ✗Forgetting to convert mixed numbers first. Multiplying or dividing with mixed numbers directly leads to errors. Always convert to improper fractions before operating.
✦ Exam tips
- →Cross-cancelling before you multiply keeps the numbers small and reduces the risk of arithmetic errors. Look for any common factor between a numerator and a denominator.
- →If the question says "Give your answer as a mixed number," you will lose the final mark if you leave it as an improper fraction.
- →On non-calculator papers, show the cross-cancelling step — it earns method marks.