Sheet № 74 · Foundation + Higher · AQA · Edexcel · OCR
Adding and Subtracting Fractions –
Adding and subtracting fractions is one of the most common skills tested in GCSE Maths. Whether it appears as a standalone question or as part of a larger problem, you need to be confident finding a common denominator and simplifying your answer.
§Key definitions
Question:
Work out 2/3 + 3/5. Give your answer as a fraction in its simplest form.
Answer:
1/12 of a cup
Q1 (Foundation):
Work out 1/4 + 2/5. Give your answer as a fraction in its simplest form.
Q2 (Foundation):
Work out 5/6 − 1/4. Give your answer as a fraction in its simplest form.
Q3 (Higher):
Work out 4 1/3 + 2 3/4. Give your answer as a mixed number.
§Formulas to memorise
a/b + c/d = (ad + bc) / bd — general method for adding fractions with different denominators
a/b − c/d = (ad − bc) / bd — general method for subtracting fractions with different denominators
LCD = LCM of the two denominators — always use the smallest common denominator to keep numbers manageable
Worked example
Work out 2/3 + 3/5. Give your answer as a fraction in its simplest form.
Working:
⚠ Common mistakes
- ✗Adding the denominators as well as the numerators. Students often write 1/3 + 1/4 = 2/7. This is wrong — you must find a common denominator first.
- ✗Using a common denominator that is not the lowest. While any common denominator works, using a larger one leads to bigger numbers and more chance of arithmetic errors.
- ✗Forgetting to simplify. Examiners expect your answer in simplest form. Always check if the numerator and denominator share a common factor.
✦ Exam tips
- →Show every step of your working — finding the LCD, converting each fraction, and simplifying. Method marks are available even if your final answer is wrong.
- →When the denominators are small, listing multiples is the quickest way to find the LCM. For larger denominators, use prime factorisation.
- →On calculator papers you can use the fraction button to check, but on non-calculator papers full working is essential.