Ratio Problems: Sharing, Changing and Combining
Solve ratio problems where a total is shared, one part is known, a ratio changes, or two ratios have to be joined through the quantity they share.
What a learner can do afterwards
- Find the total from one known part of a ratio
- Combine a : b and b : c into a : b : c through the shared term
- Work out the new ratio after a stated change to one part
1 · Read
Every ratio problem runs on one part. To share 50 pounds in ratio 3 to 2, add the parts to get 5, divide 50 by 5 to get 10 per part, and hand out 30 and 20. To find a total from one share, reverse the flow: 24 pounds covering 2 parts means 12 per part, and 5 parts make 60.
Combining ratios hinges on the shared term. With a to b as 2 to 3 and b to c as 4 to 5, b is 3 in one and 4 in the other. Scale both until b matches at 12, giving 8 to 12 to 15. Copying numbers across as 2 to 3 to 5 breaks the chain.
Changing a ratio means changing the amounts first. A 3 to 2 split of 50 pounds gives 30 and 20. Hand the first partner 10 more from outside to make 40 against 20. The new ratio 40 to 20 simplifies to 2 to 1.
Proportions solve ratio equations by cross-multiplying. If 2 parts match 14 litres of red paint, set 2 over 5 equal to 14 over w to find 35 litres of white. Read each ratio aloud first, since swapping the order on one side is the classic slip.
Find one part, match the shared term, and recompute amounts before simplifying.
2 · Watch
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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.