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GCSE Fractions Mastery Worksheet

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GCSE Fractions Mastery Worksheet

Fractions illustration

Instructions: Show all working clearly. Give all answers in their simplest form unless stated otherwise. Use the space provided for calculations.

📚 Part 1: Foundation Skills

1. Simplify these fractions:

a) 12/18 = ______ b) 15/25 = ______ c) 28/42 = ______

2. Calculate the following. Give your answers as mixed numbers where appropriate:

a) 2/3 + 1/4 = ______ b) 5/6 - 2/9 = ______

3. Work out:

a) 3/4 × 2/5 = ______ b) 2/3 ÷ 4/9 = ______

4. Convert these mixed numbers to improper fractions:

a) 2 3/5 = ______ b) 4 1/8 = ______

5. Convert these recurring decimals to fractions:

a) 0.3̇ = ______ b) 0.27̇ = ______

✏️ Part 2: Ratio and Proportion

6. A recipe uses ingredients in the ratio flour : sugar : butter = 5 : 2 : 3

If 400g of flour is used, calculate the mass of sugar and butter needed.

Sugar: ______ g Butter: ______ g

7. Two numbers are in the ratio 3 : 7. If their sum is 60, find the two numbers.

Smaller number: ______ Larger number: ______

🎯 Part 3: Exam-Style Problems

8. Sarah spends 2/5 of her monthly salary on rent and 1/4 on food. She saves £420 from the remainder.

If she saves 3/7 of what's left after rent and food, calculate her monthly salary.

9. A water tank is 3/4 full. After using 2/3 of the water in the tank, 180 litres remain.

Calculate the total capacity of the tank when full.

10. In a class, 2/5 of students walk to school, 1/3 come by bus, and the remaining 8 students cycle.

How many students are in the class? Show that your answer is correct.

📝 Answer Key

1. a) 2/3 b) 3/5 c) 2/3

2. a) 11/12 b) 7/18

3. a) 3/10 b) 3/2 or 1 1/2

4. a) 13/5 b) 33/8

5. a) 1/3 b) 3/11

6. Sugar: 160g, Butter: 240g

7. Smaller: 18, Larger: 42

8. Monthly salary: £1260

9. Total capacity: 720 litres

10. 30 students in the class

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