Fractions (GCSE Maths) - Worksheets, Questions and Revision

20 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 6)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Number - Fractions

3.2 Fractions

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Fractions

This topic covers the four operations with fractions: addition, subtraction, multiplication and division, including calculations with mixed numbers. Each operation has its own method, and mixed numbers are usually converted to improper (top-heavy) fractions before calculating.

Addition/subtraction: write both fractions with a common denominator, then add or subtract the numerators only.
Multiplication: multiply the numerators together and the denominators together, then simplify.
Division: keep the first fraction, flip (find the reciprocal of) the second fraction, then change divide to multiply.
Mixed numbers: convert to an improper fraction first (whole number x denominator + numerator, over the same denominator), calculate, then convert back to a mixed number if needed.

Worked example. Work out 2 1/3 + 1 1/4, giving your answer as a mixed number in its simplest form.

Convert to improper fractions: 2 1/3 = (2x3+1)/3 = 7/3; 1 1/4 = (1x4+1)/4 = 5/4.
Common denominator of 3 and 4 is 12: 7/3 = 28/12; 5/4 = 15/12.
Add the numerators: 28/12 + 15/12 = 43/12.
Convert back to a mixed number: 43 divided by 12 = 3 remainder 7, so 43/12 = 3 7/12.

Answer: 2 1/3 + 1 1/4 = 3 7/12.

Work out 3/8 + 2/8. Give your answer in its simplest form.

(Total for Question 1 is 1 mark)

Work out 7/9 - 4/9. Give your answer in its simplest form.

(Total for Question 2 is 2 marks)

Write 4 1/3 as an improper fraction.

(Total for Question 3 is 1 mark)

Write 29/6 as a mixed number.

(Total for Question 4 is 1 mark)

Work out 3/5 x 2/3. Give your answer in its simplest form.

(Total for Question 5 is 2 marks)

Work out 4/5 divided by 2/3. Give your answer as a mixed number in its simplest form.

(Total for Question 6 is 2 marks)

Work out 2/5 + 1/4. Give your answer as a single fraction in its simplest form.

(Total for Question 7 is 2 marks)

Work out 5/6 - 3/8. Give your answer as a single fraction in its simplest form.

(Total for Question 8 is 2 marks)

Work out 2 3/4 + 1 5/6. Give your answer as a mixed number in its simplest form.

(Total for Question 9 is 3 marks)

Work out 5 1/4 - 2 5/6. Give your answer as a mixed number in its simplest form.

(Total for Question 10 is 3 marks)

Work out 2 1/2 x 1 1/3. Give your answer as a mixed number in its simplest form.

(Total for Question 11 is 3 marks)

Work out 3 1/3 divided by 1 2/5. Give your answer as a mixed number in its simplest form.

(Total for Question 12 is 3 marks)

Priya has £84. She spends 2/7 of it on a coat. She then spends 1/4 of what remains on a book. Work out how much money Priya has left.

(Total for Question 13 is 3 marks)

A recipe for 8 people needs 2 1/2 cups of flour and 3/4 cup of sugar. Aisha wants to make enough of the recipe for 20 people.

(a)Work out how many cups of flour Aisha needs for 20 people.(2)

(b)Work out how many cups of sugar Aisha needs for 20 people.(2)

(Total for Question 14 is 4 marks)

A piece of ribbon is 96 cm long. Ben cuts off 3/8 of the ribbon.

(a)Work out the length of ribbon that Ben cuts off.(2)

(b)Chloe then cuts off 3/5 of the ribbon that remains after Ben's cut. Work out the length of ribbon that is left.(2)

(Total for Question 15 is 4 marks)

Compare the fractions 5/9 and 7/12. You must show your working, and write < , > or = between the two fractions.

(Total for Question 16 is 2 marks)

3/8 of a number is 27. Work out the number.

(Total for Question 17 is 2 marks)

In a survey of 240 people, 3/5 said they prefer tea to coffee.

(a)Work out how many people prefer tea to coffee.(2)

(b)Of the people who prefer tea, 25% take their tea with no sugar. Work out how many of the tea drinkers take their tea with no sugar.(2)

(Total for Question 18 is 4 marks)

Convert the recurring decimal 0.272727... (the digits 27 repeat forever) to a fraction in its simplest form. You must show your working.

(Total for Question 19 is 3 marks)

Rohan spends 2/5 of his monthly pay on rent. He then spends 1/4 of what remains on bills. He saves the rest of his pay, which comes to £540. Work out Rohan's monthly pay.

(Total for Question 20 is 4 marks)

Mark scheme · 3.2 Fractions

Question 1

B1 5/8 cao
Answer: 5/8

Question 2

M1 3/9 oe (subtracting the numerators, same denominator)
A1 1/3 cao (simplest form)
Answer: 1/3

Question 3

B1 13/3 cao
Answer: 13/3

Question 4

B1 4 5/6 cao
Answer: 4 5/6

Question 5

M1 (3 x 2)/(5 x 3) = 6/15 oe (multiplying numerators and denominators)
A1 2/5 cao (simplest form)
Answer: 2/5

Question 6

M1 4/5 x 3/2 oe (multiplying by the reciprocal of 2/3)
A1 1 1/5 cao
Answer: 1 1/5

Question 7

M1 8/20 + 5/20 oe (common denominator of 20 used)
A1 13/20 cao
Answer: 13/20

Question 8

M1 20/24 - 9/24 oe (common denominator of 24 used)
A1 11/24 cao
Answer: 11/24

Question 9

M1 converts both mixed numbers to improper fractions, 11/4 and 11/6
M1 33/12 + 22/12 oe (common denominator of 12 used)
A1 4 7/12 cao
Answer: 4 7/12

Question 10

M1 converts both mixed numbers to improper fractions, 21/4 and 17/6
M1 63/12 - 34/12 oe (common denominator of 12 used)
A1 2 5/12 cao
Answer: 2 5/12

Question 11

M1 converts both mixed numbers to improper fractions, 5/2 and 4/3
M1 (5 x 4)/(2 x 3) = 20/6 oe (multiplying numerators and denominators)
A1 3 1/3 cao
Answer: 3 1/3

Question 12

M1 converts both mixed numbers to improper fractions, 10/3 and 7/5
M1 10/3 x 5/7 oe (multiplying by the reciprocal of 7/5)
A1 2 8/21 cao
Answer: 2 8/21

Question 13

M1 84/7 = 12, 12 x 2 = 24 oe, the cost of the coat
M1 84 - 24 = 60 (dep), then 60/4 = 15 oe, the cost of the book
A1 45 (pounds) cao
Answer: £45

Question 14

(a) M1 scale factor 20/8 = 2.5 oe, used with 2 1/2
(a) A1 6 1/4 cups oe (e.g. 6.25 cups), cao
(a) Answer: 6 1/4 cups (6.25 cups)
(b) M1 2.5 x 3/4 oe (ft scale factor from part (a))
(b) A1 1 7/8 cups oe (e.g. 1.875 cups), cao
(b) Answer: 1 7/8 cups (1.875 cups)

Question 15

(a) M1 96/8 = 12 oe (dividing by the denominator)
(a) A1 36 (cm) cao
(a) Answer: 36 cm
(b) M1 96 - 36 = 60 (ft from part (a)), then 3/5 x 60 = 36 oe, Chloe's cut
(b) A1 24 (cm) cao
(b) Answer: 24 cm

Question 16

M1 20/36 and 21/36 oe (common denominator of 36 used, or equivalent decimal method)
A1 cao, 5/9 < 7/12
Answer: 5/9 < 7/12

Question 17

M1 27/3 = 9 oe (finding 1/8 of the number)
A1 72 cao
Answer: 72

Question 18

(a) M1 240/5 = 48 oe (dividing by the denominator)
(a) A1 144 cao
(a) Answer: 144
(b) M1 144/4 oe (ft from part (a); 25% of 144, e.g. 0.25 x 144)
(b) A1 36 cao
(b) Answer: 36

Question 19

M1 x = 0.272727..., then 100x = 27.272727... (multiplying by 100, since 2 digits repeat)
M1 100x - x = 27, so 99x = 27 oe
A1 3/11 cao (simplest form)
Answer: 3/11

Question 20

M1 identifies remainder after rent as 3/5 (of the pay) oe
M1 bills = 1/4 x 3/5 = 3/20 (of the pay) oe
M1 savings fraction = 3/5 - 3/20 = 9/20 (of the pay), leading to 9/20 x T = 540 oe
A1 1200 (pounds) cao
Answer: £1200

Mark my answers

Fractions (GCSE Maths) - Worksheets, Questions and Revision

More on this topic

Next in this strand

3.2 Fractions

Revision notes: Fractions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20