Dividing Quantities by Ratio
Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole
What a learner can do afterwards
- Share £60 between two people in the ratio 2:3 by finding the value of one part
- Express the result of sharing 24 sweets as 10 and 14 in ratio form as 5:7
- Solve problems involving three-part ratios (e.g. divide 180 in the ratio 1:2:3)
The lesson
You already know how to write a ratio and picture it with a bar model. Now you'll use that picture to split a real amount. Add the numbers in the ratio to find the total number of parts. Divide the whole amount by that total to find what one part is worth. Then multiply each ratio number by that value to get every share.
Ben and Amy share £60 in the ratio 2:3. Total parts: 2 + 3 = 5. One part: £60 ÷ 5 = £12. Ben's share: 2 × £12 = £24. Amy's share: 3 × £12 = £36. As a fraction of the whole, Ben gets 2/5 of the £60 and Amy gets 3/5.
The same idea stretches to three parts. To split 180 in the ratio 1:2:3, add the parts: 1 + 2 + 3 = 6. One part is 180 ÷ 6 = 30. The shares are 1 × 30 = 30, 2 × 30 = 60, and 3 × 30 = 90. Check by adding them back: 30 + 60 + 90 = 180.
You can also work backwards. If a split comes out as 10 and 14, write it as a ratio, 10:14, then simplify by dividing both numbers by their highest common factor, 2. That gives you 5:7.
Add the parts, divide the whole to find one part, then multiply by each ratio number to get every share.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.