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Combining ratios

Free Printable Combining ratios PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free combining ratios worksheets (PDF), GCSE maths past paper questions and worked solutions for Combining ratios (5A). This is a Grade 5 ratio & proportion topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Corbett Maths, Dr Austin, Dr Frost (B. Blocks), E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our combining ratios revision notes and worked examples with diagrams, try real GCSE past paper combining ratios questions with step-by-step solutions, or download a PDF of all combining ratios worksheet links.

Free Combining ratios PDF Worksheets & Answers

Grade 5 • Topic 5A
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Question booklet & answer sheet
 Qs Ans
Textbook Exercise & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Building Blocks skill sheet & answers
 Qs Ans
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
Online topic notes & examples
 Page
Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Combining ratios: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To combine two separate ratios such as a : b and b : c into a single three-part ratio a : b : c, identify the item that appears in both ratios (here, b). Find the lowest common multiple (LCM) of the two numbers representing that shared item.

Multiply all parts of each ratio so that the shared item has the exact same value in both ratios, then write them together as a : b : c. Once combined, you can add the parts to solve total-amount problems or compare any two quantities directly.

Example 1: Given that a : b = 2 : 3 and b : c = 4 : 5, find the ratio a : b : c in its simplest form.

Solution:

Match b using the LCM of 3 and 4, which is 12:
• Multiply a : b = 2 : 3 by 4 → 8 : 12
• Multiply b : c = 4 : 5 by 3 → 12 : 15
Combine the three parts together:
Answer: a : b : c = 8 : 12 : 15

Example 2: In a bag of 66 counters, red : blue = 3 : 2 and blue : green = 5 : 4. How many blue counters are there?

Solution:

Match blue (LCM of 2 and 5 is 10):
• R : B = 15 : 10 and B : G = 10 : 8 → 15 : 10 : 8
Total parts = 15 + 10 + 8 = 33 parts
1 part = 66 ÷ 33 = 2 counters; Blue = 10 × 2 = 20
Answer: 20 blue counters
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Combining ratios Questions & Answers

Past Paper Example 1 GCSE May 2018 1F Q20 / 1H Q2 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
In a village
[INDENT]the number of houses and the number of flats are in the ratio 7 : 4
[INDENT]the number of flats and the number of bungalows are in the ratio 8 : 5
There are 50 bungalows in the village.
How many houses are there in the village?
Worked Solution & Mark Scheme (3 marks)
Houses : Flats : Bungalows = 14 : 8 : 5. 50 ÷ 5 = 10 M1
Flats = 8 × 10 = 80 M1
Houses = 14 × 10 = 140. A1
Answer: 140
Past Paper Example 2 GCSE Nov 2022 1F Q24 / 1H Q6 6 marks
Full Paper (PDF) • Mark Scheme (PDF)
Rizwan writes down three numbers a, b and c
a : b = 1 : 3
b : c = 6 : 5
(a) Find a : b : c [2 marks]
Express a as a fraction of the total of the three numbers a, b and c [2 marks]
(b) Find m : p [2 marks]
Worked Solution & Mark Scheme (6 marks)
Part (a) Solution:
a : b = 2 : 6 M1
⇒ a : b : c = 2 : 6 : 5 A1
Answer (a): 2 : 6 : 5
Part Solution:
2 / (2 + 6 + 5) = 2/13 M1 A1
Answer : 213
Part (b) Solution:
p = 5(2m) = 10m M1
⇒ m : p = 1 : 10 A1
Answer (b): 1 : 10
Past Paper Example 3 Specimen Set 2 1F Q12 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
Helen has 80 books to sell.
Each book is Fiction or Non-fiction.
The ratio of the number of Fiction books to the number of Non-fiction books is 3:1
Each book has a normal price of £10
Helen reduces the price of all the Non-fiction books.
Non-fictionAll books½ price
Helen sells all 80 books.
Work out the total amount of money Helen will receive.
Worked Solution & Mark Scheme (4 marks)
3 + 1 = 4 parts M1
Non-fiction = 80 ÷ 4 = 20 books, Fiction = 60 books M1
Fiction = 60 × £10 = £600 M1
Non-fiction = 20 × £5 = £100
Total = £600 + £100 = £700 A1
Answer: £ 700

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