--- title: "Dividing by Fractions" description: "Interpret and compute division of a positive whole number by a positive unit fraction below 1; use visual models and the relationship between multiplication and division to explain why the quotient is" canonical: https://lightmysky.com/learn/mathematics/dividing-by-fractions-mt_1PAWhRhpdg source: https://lightmysky.com/learn/mathematics/dividing-by-fractions-mt_1PAWhRhpdg.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 by Fractions Interpret and compute division of a positive whole number by a positive unit fraction below 1; use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend. Subject: Mathematics · Area: Fractions · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/dividing-by-fractions-mt_1PAWhRhpdg ## Ready when they can - Compute 4 ÷ (1/5) = 20 and explain: 'How many fifths fit in 4 wholes?' - Create a story context for 6 ÷ (1/4) and solve it - Verify 4 ÷ (1/5) = 20 by showing 20 × (1/5) = 4 ## Lesson: Dividing a Whole Number by a Fraction You already know how to multiply fractions. Now you will divide a whole number by a fraction, like 4 ÷ 1/5. This question means: how many fifths fit inside 4 wholes? *(drawing: Every whole hides 5 fifths inside it. Cut one whole bar into 5 equal strips and you get 5 fifths.)* Work a question like that the same way: count the pieces in one whole, then multiply by how many wholes you have. Take 6 ÷ 1/5. Each whole holds 5 fifths, and you have 6 wholes, so 6 × 5 = 30 fifths. That means 6 ÷ 1/5 = 30. The answer is bigger than 6, because dividing a number above 0 by a positive fraction smaller than 1 makes more pieces. Check by multiplying back: 30 × 1/5 = 6. **Example.** Ali has 3 litres of soup. Each bowl holds 1/6 of a litre. To find how many bowls he can fill, solve 3 ÷ 1/6. Each whole litre holds 6 sixths, and he has 3 litres, so 3 × 6 = 18 bowls. **Tip.** There are two ways to check your work. First, dividing by a fraction is the same as multiplying by how many of those pieces fit in one whole (6 ÷ 1/5 = 6 × 5). Second, multiply your answer back: 30 × 1/5 = 6. If you land back on the number you started with, the division is correct. **Recap.** Dividing a number bigger than 0 by a positive fraction smaller than 1 always gives a bigger answer, because you are counting how many tiny pieces fit inside the whole. ## Practice 19 questions on this page, each with its working shown. ## Needs first - [Fractions of a whole (age 10+)](https://lightmysky.com/learn/mathematics/fractions-of-a-whole-age-10-mt_4Km38F4L-6) - [Multiplying fractions (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi) - [Dividing fractions (unit fractions)](https://lightmysky.com/learn/mathematics/dividing-fractions-unit-fractions-mt_ifPDOYvUqm) ## Opens up - [Dividing unit fractions and whole numbers](https://lightmysky.com/learn/mathematics/dividing-unit-fractions-and-whole-numbers-mt_rCMdwG-YOE)