Sheet № 01 · Foundation + Higher · AQA · Edexcel · OCR
Fractions –
Fractions are one of the most fundamental topics in GCSE Maths and appear across every exam board — AQA, Edexcel, and OCR. Whether you are sitting Foundation or Higher tier, you need to be confident with adding, subtracting, multiplying, and dividing fractions, as well as converting between improper fractions and mixed numbers. This page
§Key definitions
Question:
Work out 2/5 + 3/4. Give your answer as a fraction in its simplest form.
Q1 (Foundation):
Work out 5/6 − 1/3. Give your answer in its simplest form.
Q2 (Foundation):
Calculate 3/7 × 2/5.
Q3 (Higher):
Work out 3 1/2 ÷ 2 1/3. Give your answer as a mixed number in its simplest form.
§Formulas to memorise
To add or subtract fractions, find a common denominator: a/b + c/d = (ad + bc) / bd
To multiply fractions: a/b × c/d = ac / bd
To divide fractions, flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c = ad / bc
To convert a mixed number to an improper fraction: whole × denominator + numerator, all over the denominator
Proper fraction — the numerator is smaller than the denominator, e.g. 3/4.
Improper fraction — the numerator is equal to or larger than the denominator, e.g. 7/3.
Mixed number — a whole number combined with a proper fraction, e.g. 2 1/3.
Worked example
Work out 2/5 + 3/4. Give your answer as a fraction in its simplest form.
Working:
⚠ Common mistakes
- ✗Forgetting to find a common denominator when adding or subtracting. You cannot simply add numerators and denominators — 1/3 + 1/4 is NOT 2/7. Always find the LCD first.
- ✗Not converting mixed numbers to improper fractions before multiplying or dividing. Working directly with mixed numbers leads to errors. Convert first, then operate.
- ✗Forgetting to simplify the final answer. Examiners expect answers in their simplest form unless stated otherwise. Always check if the numerator and denominator share a common factor.
- ✗Flipping the wrong fraction when dividing. Remember: Keep, Change, Flip — keep the first fraction, change ÷ to ×, flip the second fraction only.
- ✗Losing negative signs. When one or both fractions are negative, track the sign carefully through each step.
✦ Exam tips
- →Show every step. Even if you can do the calculation mentally, writing each step earns method marks if your final answer is wrong.
- →Simplify at the end or cross-cancel early. Both approaches are valid, but cross-cancelling before you multiply keeps numbers small and reduces arithmetic errors.
- →Check whether the question asks for a fraction, mixed number, or decimal. Giving the answer in the wrong form can cost you the final accuracy mark.
- →Use fractions on your calculator wisely. On calculator papers, the fraction button can verify your answer, but on non-calculator papers you must show full working. See our formulas guide for more on what to memorise.
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