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.

What Is Adding and Subtracting Fractions?

When two fractions share the same denominator, you simply add or subtract the numerators and keep the denominator. For example, 3/8 + 2/8 = 5/8. The challenge arises when the denominators are different — you cannot add 2/5 and 1/3 directly because the parts are different sizes.

To handle different denominators you must rewrite both fractions so they share a lowest common denominator (LCD). The LCD is the lowest common multiple (LCM) of the two denominators. Once both fractions have the same denominator, the addition or subtraction becomes straightforward.

If the question involves mixed numbers, convert them to improper fractions first, perform the operation, then convert back to a mixed number if the question requires it.

Key Formulas

Step-by-Step Method

1. Check whether the denominators are the same. If they are, add or subtract the numerators directly.
2. If the denominators differ, find the LCD (the LCM of the denominators).
3. Multiply the numerator and denominator of each fraction so both have the LCD as their denominator.
4. Add or subtract the numerators. Keep the denominator unchanged.
5. Simplify the resulting fraction by dividing numerator and denominator by their HCF.
6. If the result is an improper fraction, convert to a mixed number when the question asks for one.

Worked Example 1 — Foundation Level

Question: Work out 2/3 + 3/5. Give your answer as a fraction in its simplest form.

Working:

Step 1 — The denominators are 3 and 5. The LCM of 3 and 5 is 15, so the LCD is 15.

Step 2 — Convert each fraction: 2/3 = 10/15 and 3/5 = 9/15.

Step 3 — Add the numerators: 10/15 + 9/15 = 19/15.

Step 4 — Convert to a mixed number: 19/15 = 1 4/15. The fraction 4/15 cannot be simplified.

Answer: 1 4/15

Worked Example 2 — Higher Level

Question: Work out 3 2/3 − 1 5/6. Give your answer as a mixed number in its simplest form.

Working:

Step 1 — Convert to improper fractions: 3 2/3 = 11/3 and 1 5/6 = 11/6.

Step 2 — The LCD of 3 and 6 is 6. Convert: 11/3 = 22/6.

Step 3 — Subtract: 22/6 − 11/6 = 11/6.

Step 4 — Convert to a mixed number: 11/6 = 1 5/6. This is already in its simplest form.

Answer: 1 5/6

Worked Example 3 — Exam Style

Question: A recipe needs 3/4 of a cup of sugar and 2/3 of a cup of flour. How much more sugar than flour is needed? (2 marks)

Working:

Step 1 — Find the LCD of 4 and 3. The LCM is 12.

Step 2 — Convert: 3/4 = 9/12 and 2/3 = 8/12.

Step 3 — Subtract: 9/12 − 8/12 = 1/12.

Answer: 1/12 of a cup

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.

Practice Questions

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.

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Related Topics

• Fractions
• Prime Factorisation, HCF and LCM
• Multiplying and Dividing Fractions

Summary

• To add or subtract fractions, both must share the same denominator.
• The lowest common denominator is the LCM of the two denominators.
• Convert each fraction, then add or subtract the numerators only.
• Convert mixed numbers to improper fractions before calculating.
• Always simplify your final answer by dividing by the HCF.