Multiple Ratios (Edexcel IGCSE Maths A) : Revision Note
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
Convert to a percentage
Multiply by 100 and round to 3 significant figures
53.6 % of the socks are black
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