Fractions Worksheet - A-Level - Intermediate
Fractions worksheet for A-Level / Vocational (Ages 16-18). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Mastering Fractions: An Advanced Exploration
A-Level Maths: Intermediate Fractions
Instructions: This worksheet is designed to deepen your understanding of fractions at an A-Level standard. Work through each activity carefully, showing all your calculations and reasoning. Use the answer spaces provided to write your answers clearly.
Simplifying Complex Fractions
Simplify each of the following complex fractions. Show all steps of your working clearly. Ensure your final answer is in its simplest form.
1. (3/4) / (9/16)
2. (5/8) / (15/32)
3. (7/10) / (14/25)
4. (2/3) / (8/27)
5. (9/11) / (27/22)
Adding and Subtracting Mixed Fractions
Perform the addition or subtraction for each pair of mixed fractions. Convert your answers to improper fractions where necessary and simplify.
1. 3 1/2 + 2 3/4
2. 5 2/3 - 3 5/6
3. 4 7/8 + 1 1/2
4. 6 3/5 - 2 2/7
5. 7 1/4 + 3 2/3
Fractional Equations
Solve each equation for x. Show all steps in your working and ensure your final answer is simplified.
1. (x/3) + 1/2 = 5/6
2. 2x/5 - 1/4 = 3/10
3. 3/7 = (2x + 1)/14
4. (x - 1)/4 = 5/8
5. 1/3 = (x + 2)/9
Multiplying Fractions in Algebraic Expressions
Expand and simplify the following algebraic expressions involving fractions. Show all steps clearly.
1. (2/3)x * (3/4)y
2. (5/6)(x + 3) * (2/5)
3. (4/7)x * (7/8)y
4. (3/5)(x - 2) * (5/9)
5. (6/11)x * (11/12)y
Fractional Inequalities
Solve the following inequalities involving fractions. Express your answers in interval notation.
1. (x/4) < 3/2
2. 5/6 > (2x - 1)/3
3. (x + 2)/5 ≥ 7/10
4. 1/3 ≤ (x - 4)/6
5. (2x + 3)/7 > 1/2
Word Problems with Fractions
Read each problem carefully and solve using fractions. Show all your working and provide your final answer in a simplified form.
1. A recipe requires 2/3 cup of sugar. If you want to make 1 1/2 times the recipe, how much sugar is needed in total?
2. A car travels 3/4 of a journey in 2 hours. How long will it take to complete the entire journey at the same speed?
3. A tank is 5/8 full. If 1/4 of the tank is used, what fraction of the tank remains?
4. A piece of ribbon is 7 1/2 metres long. If 2/3 is cut off, how much ribbon is left?
5. A cyclist covers 2/5 of a distance in 1 hour. How much distance will be covered in 3 hours at the same speed?
Activity 1: 4/3 ; 4/3 ; 5/4 ; 9/4 ; 2/3
Activity 2: 6 1/4 ; 1 5/6 ; 6 3/8 ; 4 11/35 ; 10 11/12
Activity 3: x = 1 ; x = 3/2 ; x = 1 ; x = 7/8 ; x = 1
Activity 4: (1/2)xy ; (1/3)(x + 3) ; (1/2)xy ; (1/3)(x - 2) ; (1/2)xy
Activity 5: x < 6 ; x < 2 ; x ≥ 1 ; x ≥ 6 ; x > 1.75
Activity 6: 1 cup ; 8/3 hours ; 3/8 ; 2 1/2 metres ; 6/5
📚 Great books for Maths
Handpicked books to support learning at home · Amazon affiliate links
CGP KS2 Maths SATs Revision Book
Year 6 maths revision with practice questions and answers
Usually ships in 24hrs
CGP KS1 Maths Workbook
Fun maths practice for ages 5–7 covering number, shape and measures
Usually ships in 24hrs
Maths Age 7–9 - Carol Vorderman
Step-by-step maths workbook for primary school children
Usually ships in 24hrs
Times Tables Practice Pad
Daily times table drills with colourful sticker rewards
Usually ships in 24hrs