Multiple Ratios (Edexcel IGCSE Maths A) : Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

Multiple Ratios

How do I combine two ratios to make a three-part ratio?

  • Identify the link between the two different ratios 

  • Find equivalent ratios for both original ratios, where the value of the link is the same

  • Join the two, two-part ratios into a three-part ratio

  • Suppose that on a farm with 85 animals

    • The ratio of cows to sheep is 2:3

    • The ratio of sheep to pigs is 6:7

    • We want to find the number of each animal on the farm

  • We need to find a combined, 3-part ratio that shows the relative portions of all the animals together

  • Notice that sheep appear in both ratios, so we can use sheep as the link between the two

    • C:S = 2:3 and S:P = 6:7

    • We can multiply both sides of the C:S ratio by 2, so that both ratios are comparing relative to 6 sheep

    • C:S = 4:6 and S:P = 6:7

    • These can now be joined together

    • C:S:P = 4:6:7

  • We can now use this to share the 85 animals in the ratio 4:6:7

    • There are 17 parts in total (4 + 6 + 7 = 17)

    • Each part is worth 5 animals (85 ÷ 17 = 5)

    • There are 20 cows (4 × 5), 30 sheep (6 × 5), and 35 pigs (7 × 5)

Worked Example

In Jamie’s sock drawer the ratio of black socks to striped socks is 5 : 2 respectively. The ratio of striped socks to white socks in the drawer is 6 : 7 respectively.

Calculate the percentage of socks in the drawer that are black.

Write down the ratios

B : S = 5 : 2
S : W = 6 : 7

S features in both ratios, so we can use it as a link
Multiply the B : S ratio by 3 to find an equivalent ratio
Both ratios are now comparing to 6 striped socks

B : S = 15 : 6
S : W = 6 : 7

Link them together

B : S : W = 15 : 6 : 7

Find the total number of parts

15 + 6 + 7 = 28

This means 15 out of 28 socks are black
Find 15 out of 28 as a decimal by completing the division

15 over 28 equals 0.535 space 714 space 285 space...

Convert to a percentage
Multiply by 100 and round to 3 significant figures

53.6 % of the socks are black

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Naomi C

Author: Naomi C

Expertise: Maths Content Creator

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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