Multiple-Ratios Aqa Higher

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)