GCSE specification fit
A core calculation skill used across GCSE Maths.
Fraction operations appear in direct number questions and inside ratio, probability, algebra, exact values and multi-step problem solving.
What you will learn
Why this matters
Fractions are not just a Number topic. They appear in probability, ratio, algebra, exact trigonometry, surds and formula work.
The key is knowing which method belongs to which operation. Addition and subtraction need common denominators. Multiplication and division do not.
Prior knowledge
You should already be comfortable with:
Clear explanation
Adding and subtracting
To add or subtract fractions, first make the denominators the same.
Multiplying
To multiply fractions, multiply the numerators and multiply the denominators.
23 × 57 = 1021Dividing
To divide by a fraction, multiply by its reciprocal. The reciprocal is the fraction turned upside down.
Mixed numbers
Mixed numbers are often easier to calculate with after changing them to improper fractions.
123 = 53Worked examples
Example 1: Add 25 and 110.
25 = 410 410 + 110 = 510 = 12Example 2: Multiply 34 by 29.
34 × 29 = 636 = 16Example 3: Divide 45 by 23.
45 ÷ 23 = 45 × 32 = 1210 = 65Quick checks
Choose an answer, then check your thinking.
1. What is 13 + 16?
2. What is 25 × 34?
3. What is 56 ÷ 13?
Practice questions
Question 1
Calculate 38 + 14.
Reveal answer and marking guidance
Answer: 58.
Marking: Change one quarter to two eighths, then add.
Question 2
Calculate 710 − 15.
Reveal answer and marking guidance
Answer: 12.
Marking: Change one fifth to two tenths, then subtract.
Question 3
Calculate 56 × 310.
Reveal answer and marking guidance
Answer: 14.
Marking: Multiply to get 1560, then simplify.
Question 4
Calculate 23 ÷ 45.
Reveal answer and marking guidance
Answer: 56.
Marking: Multiply 23 by 54.
Question 5
Calculate 112 × 25.
Reveal answer and marking guidance
Answer: 35.
Marking: Change 112 to 32, then multiply.
Question 6
Calculate −34 + 56.
Reveal answer and marking guidance
Answer: 112.
Marking: Use twelfths: −912 + 1012 = 112.
Question 7
Calculate 56 − 13 × 34.
Reveal answer and marking guidance
Answer: 712.
Marking: Multiply first: 13 × 34 = 14. Then subtract using twelfths: 1012 − 312 = 712.
Question 8
A recipe uses 34 kg of flour. You make 23 of the recipe. How much flour is needed?
Reveal answer and marking guidance
Answer: 12 kg.
Marking: Find a fraction of an amount by multiplying: 23 × 34 = 12. Include kg in the final answer.
Question 9
Calculate 214 − 35 ÷ 67.
Reveal answer and marking guidance
Answer: 11120.
Marking: Do the division first: 35 ÷ 67 = 35 × 76 = 710. Then 94 − 710 = 4520 − 1420 = 3120 = 11120.
Question 10
A tank is 35 full. A pump removes 27 of the water currently in the tank. What fraction of the whole tank is removed?
Reveal answer and marking guidance
Answer: 635 of the whole tank.
Marking: Find a fraction of a fraction by multiplying: 27 × 35 = 635. The answer is already simplified.
Answers and marking guidance
The exact practice answers are hidden under each question so you can try first. For fraction calculations, marks usually come from choosing the correct method for the operation: common denominators for adding or subtracting, improper fractions for mixed numbers, multiplying straight across for multiplication, using the reciprocal for division, handling signs carefully and simplifying the final answer where possible. In mixed calculations, show the operation order so the examiner can see why you multiplied or divided before adding or subtracting.
Common mistakes
- Adding denominators: 13 + 16 is not 29.
- Using a common denominator for multiplication: multiply fractions directly, then simplify.
- Flipping the wrong fraction: in division, only flip the fraction you are dividing by.
- Forgetting to simplify: check for a common factor in the final answer.
Extension challenge
Calculate 34 − 25 × 58.
Reveal answer
Answer: 12.
Do the multiplication first: 25 × 58 = 14. Then 34 − 14 = 12.
Exam-board guidance
Fraction operations are assessed across GCSE Maths as exact arithmetic, often inside ratio, probability, algebra, measures or calculator/non-calculator questions.
AQA GCSE Maths
Fraction operations may appear as direct calculations or inside longer number, ratio and exact-answer questions; show common-denominator, improper-fraction or reciprocal working clearly.
OCR GCSE Maths
Practise all four operations, including mixed and negative fractions, and decide when to use a common denominator, improper fraction or reciprocal.
Pearson Edexcel GCSE Maths
Show enough fraction working for the operation to be clear, then simplify or convert mixed-number answers only when suitable.
Eduqas GCSE Maths
Accurate method matters, so use common denominators for adding and subtracting, improper fractions for mixed numbers and reciprocals only for division.
WJEC Wales
Fraction operations are part of calculation fluency and may appear in practical numeracy contexts involving measures, money or rates.
CCEA GCSE Maths
Begin with simple fraction operations, then apply the same skills in unit problems involving fractions, decimals, percentages and calculator/non-calculator decisions.
Next lesson
Next, practise reading, comparing and rounding decimal numbers.