Foundation and Higher · sharing in a ratio
Share in a ratio.
Find one part
first.
the bar model
does the thinking
every ratio question comes down to —
One part
find what one part is worth
then multiply
type 1 of 4
Given the total
1. 3 + 5 = 8 parts altogether.
2. 40 ÷ 8 = 5, so each part is £5.
✓ 3 × 5 = 15 and 5 × 5 = 25
share £40 in the ratio 3 : 5
type 2 of 4
Given one share
1. The 12 is spread over 2 parts.
2. 12 ÷ 2 = 6, so each part is 6.
✓ 3 parts: 3 × 6 = 18
ratio 2 : 3, the smaller share is 12
type 3 of 4
Given the difference
1. The difference is 7 − 3 = 4 parts.
2. 4 parts = 20, so one part is 5.
✓ 3 × 5 = 15 and 7 × 5 = 35
ratio 3 : 7, the difference is 20
type 4 of 4
Three-way ratio
1. Same method: 1 + 2 + 3 = 6 parts.
2. 60 ÷ 6 = 10 per part.
✓ 10, 20 and 30. Check: they add to 60
share 60 in the ratio 1 : 2 : 3
sharing in a ratio —
Total given
÷ by the total number of parts
One share given
÷ by that share’s parts
Difference given
÷ by the difference in parts
Find one part.
Everything else is multiplying.
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