Where can I download free operations with fractions PDF worksheets with answers?

On this MathsLinks page you can download free printable operations with fractions PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from MathsLinks, Ken Stafford, Ken Stafford (1), Ken Stafford (2), Maths Genie, plus a printable one-page operations with fractions revision guide.

What GCSE grade is operations with fractions (3B)?

Operations with fractions (topic code 3B) is a Grade 3 number topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Operations with fractions Worksheets (PDF) with Answers — GCSE Maths

Free Operations with fractions PDF Worksheets & Answers

Grade 3 • Topic 3B

Resource	Questions	Answers
MathsLinks Operations with fractions questions & answers	Qs	Ans
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Ken Stafford (2) Practice worksheet & worked solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths DIY Exam-style booklet & solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Metatutor (2) Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
MathsLinks Interactive 10-question revision grid	Grid
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 3 topics
3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables

Explanation:

Before adding, subtracting, multiplying, or dividing mixed numbers, always convert any mixed numbers into improper (top-heavy) fractions first. To add or subtract fractions, find a common denominator, convert both numerators, and then add or subtract the numerators only.

To multiply fractions, multiply the numerators together and multiply the denominators together. To divide by a fraction, use Keep, Change, Flip: keep the first fraction, change ÷ to ×, and flip the second fraction upside down. Simplify your final answer and convert back to a mixed number if required.

Example 1: Work out 234 − 125

Solution:

Improper fractions: 114 − 75

Common denominator of 4 and 5 is 20:

= 5520 − 2820 = 2720

Answer: 1720

Example 2: Work out 145 ÷ 310

Solution:

Improper fraction: 145 = 95

Keep, Change, Flip: 95 × 103

Multiply across: 9 × 105 × 3 = 9015

Answer: 6

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Operations with fractions Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 Specimen Set 2 1H Q6 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Work out
(a) Work out 2 1/4 × 3 1/3 (3) (b) Place 3, 4, 5 and 6 in the boxes for greatest total. (1)

(a) Work out 214 × 313
Give your answer as a mixed number in its simplest form. [3 marks]

(b) Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total.
You may write each number only once. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

9/4 × 10/3 = 90/12 = 15/2 = 7 1/2 M2 A1

Answer (a): 712

Part (b) Solution:

Largest whole numbers are 5 and 6
put smaller denominator 3 under larger numerator 2: 5 1/4 + 6 2/3 = 11 11/12 B1

Answer (b): 514 + 623

Past Paper Example 2 OCR Jun 2025 3F Q12 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows a large rectangle made from 10 smaller rectangles of equal area.
The large rectangle is divided into two unequal parts, A and B.

(a) Tick (✓) all the correct statements.
@@TABULAR₀@@ [2 marks]

(b) The area of Part A is 18k.
Write an expression, in terms of k, for the area of Part B.
Give your answer in its simplest form. [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

(The area of a rectangle is length × width)
Part A has 3 small rectangles and Part B has 7 small rectangles out of 10 M1
So A : B = 3 : 7 and A is 3/10 of the large rectangle. A1

Answer (a): Tick 2nd row (A : B = 3 : 7) and 3rd row (A is 3/10 of the large rectangle)

Part (b) Solution:

(The area of a rectangle is length × width)
1 small rectangle = 18k ÷ 3 = 6k M1
Area of Part B (7 small rectangles) = 7 × 6k = 42k. A1

Answer (b): 42k

Past Paper Example 3 AQA Jun 2018 1F Q7 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

A rectangular carpet measures 8 m by 6 m
Part of the carpet is covered by a square rug of length 2 m

Show that 112 of the carpet is covered by the rug.

Worked Solution & Mark Scheme (2 marks)

Area of carpet = 8 × 6 = 48 m² M1
Area of rug = 2 × 2 = 4 m²
Fraction of carpet covered = 448 = 112 C1

← 3A Error intervals

Back to GCSE questions by topic

3C Estimation →

Operations with fractions

Free Operations with fractions PDF Worksheets & Answers

Guide to Operations with fractions: Explanation, Diagrams & Worked Examples

GCSE Past Paper Operations with fractions Questions & Answers