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

On this MathsLinks page you can download free printable algebraic fractions PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from MathsLinks, Ken Stafford, Maths Genie, Maths4Everyone (1), Maths4Everyone (2), plus a printable one-page algebraic fractions revision guide.

What GCSE grade is algebraic fractions (7D)?

Algebraic fractions (topic code 7D) is a Grade 7 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

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

Free Algebraic fractions PDF Worksheets & Answers

Grade 7 • Topic 7D

Resource	Questions	Answers
MathsLinks Algebraic fractions questions & answers	Qs	Ans
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone (1) GCSE 9–1 practice booklet & solutions	Qs	Ans
Maths4Everyone (2) GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
1st Class Maths (1) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (2) Edexcel exam questions & solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & 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
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 7 topics
7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment

Explanation:

Never cancel individual terms across a + or − sign; always factorise the numerator and denominator fully first, then cancel common bracketed factors. When multiplying fractions, factorise and cancel diagonally or vertically; when dividing, flip the second fraction and multiply.

To add or subtract algebraic fractions, rewrite both fractions over their lowest common denominator (usually the product of their linear denominators), expand the numerators carefully (watching out for a minus sign in front of a bracket), and simplify.

Example 1: Simplify fully 2x² + 5x − 3x² − 9

Solution:

Factorise numerator: 2x² + 6x − x − 3 = (2x − 1)(x + 3)

Factorise denominator (DOTS): x² − 9 = (x − 3)(x + 3)

= (2x − 1)(x + 3)(x − 3)(x + 3)

Cancel common factor (x + 3):

Answer: 2x − 1x − 3

Example 2: Write 4x − 2 − 3x + 1 as a single fraction.

Solution:

Common denominator is (x − 2)(x + 1):

= 4(x + 1) − 3(x − 2)(x − 2)(x + 1)

Expand top: 4x + 4 − 3x + 6 = x + 10

Answer: x + 10(x − 2)(x + 1)

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Algebraic fractions Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jun 2025 1H Q12 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Express 54 + x - 36x as a single fraction in its simplest form.

Worked Solution & Mark Scheme (3 marks)

15x / 12x + 2(x – 3) / 12x = (15x + 2x – 6) / 12x = (17x – 6) / 12x M2 A1

Answer: 17x - 612x

Past Paper Example 2 AQA Nov 2023 3H Q22 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Write 72a² - 35a as a single fraction in its simplest form.

Worked Solution & Mark Scheme (2 marks)

Common denominator is 10a²: M1
(7 × 5) / (10a²) – (3 × 2a) / (10a²) = (35 – 6a) / (10a²). A1

Answer: Answer 35 - 6a10a²

Past Paper Example 3 GCSE Nov 2018 2H Q12 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Simplify [(4x² – 9)/(6x + 9)] × [2x/(x² – 3x)] in the form (ax + b)/(cx + d). (3) (b) Express 3/(x + 1) + 1/(x – 2) – 4/x as a single fraction. (3)

(a) Write 4x² - 96x + 9 × 2xx² - 3x in the form ax + bcx + d where a, b, c and d are integers. [3 marks]

(b) Express 3x + 1 + 1x - 2 - 4x as a single fraction in its simplest form. [3 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

[(2x – 3)(2x + 3) / 3(2x + 3)] × [2x / x(x – 3)] = 2(2x – 3) / 3(x – 3) = (4x – 6)/(3x – 9) M2 A1

Answer (a): 4x - 63x - 9

Part (b) Solution:

[3x(x – 2) + x(x + 1) – 4(x + 1)(x – 2)] / [x(x + 1)(x – 2)] = (3x² – 6x + x² + x – 4x² + 4x + 8) / [x(x + 1)(x – 2)] = (8 – x) / [x(x + 1)(x – 2)] M2 A1

Answer (b): 8 - xx(x + 1)(x - 2)

← 7C Proportion (harder)

Back to GCSE questions by topic

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Algebraic fractions

Free Algebraic fractions PDF Worksheets & Answers

Guide to Algebraic fractions: Explanation, Diagrams & Worked Examples

GCSE Past Paper Algebraic fractions Questions & Answers