--- title: "Dividing Quantities by Ratio" description: "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" canonical: https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z source: https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z.md retrieved: 2026-10-19 --- > **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`. # 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 Subject: Mathematics · Area: Ratio & Proportion · Ages 11 to 13 Page: https://lightmysky.com/learn/mathematics/dividing-quantities-by-ratio-mt_nOCPx5qw0Z ## Ready when they can - 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) ## Lesson: Dividing Quantities by Ratio 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. *(drawing: 5 parts make £60, so one part is £12. Two parts is £24, three parts is £36.)* **Example.** 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. **Tip.** 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. **Recap.** Add the parts, divide the whole to find one part, then multiply by each ratio number to get every share. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Proportional Reasoning Vocabulary](https://lightmysky.com/learn/mathematics/proportional-reasoning-vocabulary-mt_ATYLKt0je-) - [Bar Models for Ratios](https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU) - [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It) ## Opens up - [Proportion](https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA) - [Ratio Problems: Sharing, Changing and Combining](https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv)