Where can I download free writing and simplifying ratio PDF worksheets with answers?

On this MathsLinks page you can download free printable writing and simplifying ratio PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Maths Genie, Corbett Practice, Corbett Textbook, Maths4EveryOne, Dr Austin, plus a printable one-page writing and simplifying ratio revision guide.

What GCSE grade is writing and simplifying ratio (3D)?

Writing and simplifying ratio (topic code 3D) is a Grade 3 ratio & proportion topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Writing and simplifying ratio Worksheets (PDF) with Answers — GCSE Maths

Free Writing and simplifying ratio PDF Worksheets & Answers

Grade 3 • Topic 3D

Resource	Questions	Answers
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths4EveryOne Structured worksheet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	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
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:

A ratio compares the sizes of parts to each other. Write the numbers in the exact order stated in the question, separated by a colon (:). If quantities have different units (such as cm and m, or g and kg), convert them into the same unit before simplifying.

To simplify a ratio to its simplest form, divide all parts by their highest common factor (HCF) until the parts are whole numbers with no common factor. To write a ratio in the form 1 : n or n : 1, divide both sides by the number that needs to become 1.

Example 1: Simplify the ratio 45 minutes : 2 hours fully.

Solution:

Convert 2 hours into minutes: 2 × 60 = 120 minutes

Ratio in same units = 45 : 120

Divide both sides by HCF (15):

45 ÷ 15 = 3 and 120 ÷ 15 = 8

Answer: 3 : 8

Example 2: Write the ratio 5 : 18 in the form 1 : n.

Solution:

To make the left-hand side equal to 1, divide both parts by 5:

Left side: 5 ÷ 5 = 1

Right side: 18 ÷ 5 = 3.6

Answer: 1 : 3.6

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Writing and simplifying ratio Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE May 2024 1F Q10 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

There are 24 cows and 36 sheep on a farm.
Write as a ratio the number of cows to the number of sheep.
Give your ratio in its simplest form.

Worked Solution & Mark Scheme (2 marks)

24 : 36 ÷ 12 = 2 : 3 M1 A1

Answer: 2 : 3

Past Paper Example 2 GCSE Nov 2023 2F Q10 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

There are 24 red counters and 40 blue counters in a bag.
Write down the ratio of the number of red counters to the number of blue counters in the bag.
Give your ratio in its simplest form.

Worked Solution & Mark Scheme (2 marks)

24 : 40 = 3 : 5 (dividing by 8) M1 A1

Answer: 3 : 5

Past Paper Example 3 Specimen Set 2 2F Q18 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

There are 64 cards in a pack.
Each card is either red or black.
The ratio of the number of red cards to the number of black cards is 1 : 1
8 red cards are removed from the pack.
Find the ratio of the number of red cards now in the pack to the number of black cards now in the pack.
Give your answer in its simplest form.

Worked Solution & Mark Scheme (3 marks)

Initially 32 red and 32 black cards M1
After removing 8 red cards: 32 – 8 = 24 red cards M1
Ratio = 24 : 32 = 3 : 4 A1

Answer: 3 : 4

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