--- title: "Ratio Problems: Sharing, Changing and Combining" description: "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." canonical: https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv source: https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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. Subject: Mathematics · Area: Ratio & Proportion · Ages 14 to 15 Page: https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv ## Ready when they can - 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 ## Lesson: Sharing by ratio 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. **Example.** 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. **Tip.** 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. **Recap.** Find one part, match the shared term, and recompute amounts before simplifying. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Compound Units](https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5) - [Dividing Quantities by Ratio](https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z) - [Ratio Notation and Relationships](https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m) ## Opens up - [Direct Proportion as a Formula](https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz)