Share an amount in a ratio, work from one share or the difference between shares, combine two ratios, and (Higher) solve problems where a ratio changes.
What you will learn
- Share an amount in a given ratio
- Find the other share or the total from one share or from the difference
- Combine a : b and b : c into one ratio
- Solve problems where a ratio changes (Higher)
Find one part first
To share £72 in the ratio 3 : 5, count the parts, find one part, then multiply.
- 3 + 5 = 8 parts
- one part = £72 ÷ 8 = £9
- first share = 3 × £9 = £27
- second share = 5 × £9 = £45
- check: £27 + £45 = £72
The same idea works backwards. If the ratio is 3 : 5 and the first share is £27, then 3 parts = £27, so one part is £9. If instead the second gets £18 more than the first, the difference is 5 − 3 = 2 parts, so one part is £18 ÷ 2 = £9. The £18 is two parts, not one: that is the usual slip. Once you know one part, the total is one part × the total number of parts: here £9 × 8 = £72.
Three parts work the same way. To share 150 sweets in the ratio 2 : 3 : 5, there are 2 + 3 + 5 = 10 parts, so one part is 15 sweets and the shares are 30, 45 and 75. The third person gets 5 − 2 = 3 parts more than the first, which is 3 × 15 = 45 sweets more.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Find one part first
- Which ingredient runs out first?
- Combining two ratios
- When the ratio changes (Higher)
- Try it: Share it
8 practice questions, marked as you go; about 25 minutes in all.
In this unit: Ratio and proportion
Convert units and use scales, write and simplify ratios, share amounts in a ratio, compare best buys and exchange rates, and solve direct and inverse proportion problems.