Combining and Splitting

Imagine you're baking: the recipe needs ½ cup of sugar plus ¾ cup later. How much sugar total? Or you have ⅔ of a pizza to share equally between 4 friends. Fraction operations let us combine, separate, scale, and share parts accurately - essential for recipes, measurements, and fair division.

Exam tip

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Common Mistakes to Avoid

❌ Wrong: 1/2 + 1/3 = 2/5 ✅ Right: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Can't add numerators and denominators separately

❌ Wrong: 2/3 × 3/4 = 6/7 ✅ Right: 2/3 × 3/4 = 6/12 = 1/2

Multiply tops together, bottoms together

❌ Wrong: 3/4 ÷ 1/2 = 3/8 ✅ Right: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2

Must flip second fraction when dividing

❌ Wrong: Not simplifying final answer ✅ Right: Always give in simplest form

6/8 should be 3/4 - marks lost!

Now try it yourself

Quiz · Question 1 of 14

Which of these fractions is the largest? ⅔ ¾ ⅗ ⅝

Tap an answer to check it

This topic in real past papers

Every real exam question we've found on fraction operations, with a full worked answer.

AQA Paper 1

Every sitting we have full papers for opens with at least one quick non-calculator arithmetic question involving fractions, decimals, or both.

1 marks

AQA Paper 2

Two of the four sittings we have full papers for test finding a reciprocal directly, once for a number with a power and once for a simple fraction.

1 marks

Edexcel Paper 1

Two of the three sittings we have full papers for open with a pure non-calculator arithmetic question, and June 2023 tests it twice in the first two questions of the paper.

3 marks

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Fraction Operations

Combining and Splitting

Combining and Splitting

Earn the mark scheme marks

Common Mistakes to Avoid

This topic in real past papers

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