--- title: "Equivalent fractions (age 9+)" description: "Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths" canonical: https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl source: https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl.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`. # Equivalent fractions (age 9+) Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths Subject: Mathematics · Area: Fractions · Ages 9 to 10 Page: https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl ## Ready when they can - Use a fraction strip to show 2/3 = 4/6 = 6/9 - Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged - Generate three fractions equivalent to 3/5 and verify with diagrams ## Lesson: Scaling a fraction's name up and down You already know 2/3 and 4/6 name the same amount. Here's why: if you cut every part of a fraction into the same number of smaller pieces, the shaded amount doesn't change, only the number of pieces does. Multiply the numerator and the denominator by the same number, and you get an equivalent fraction. *(drawing: Cut each of these 3 parts into 2 smaller pieces. Now there are 6 parts, and 4 are shaded. That's 4/6, the exact same amount as 2/3.)* **Example.** Priya wants a fraction equivalent to 3/5. She multiplies the numerator and denominator by 2: 3 x 2 = 6, and 5 x 2 = 10. So 3/5 = 6/10. Names go down as well as up. Priya has another bed of 12 squares with 8 of them planted: 8/12. She groups the 12 squares into 3 blocks of 4, and 2 whole blocks are planted. That is 2/3, the same planting with a smaller name. Divide the numerator and the denominator by the same number and the amount stays put. **Example.** Which is more, 3/5 or 5/10? The 5 on top looks bigger than the 3, but fifths and tenths are different sizes, so the top numbers alone cannot settle it. Give both the same bottom number first: 3/5 = 6/10. Now every piece is a tenth, so compare the tops. 6 tenths is more than 5 tenths, so 3/5 is more. **Tip.** Whatever you do to the numerator, do to the denominator: multiply both by the same number, or divide both by the same number. Change only one of them and the value of the fraction changes. **Recap.** Multiply or divide the numerator and denominator by the same number, and the fraction's value stays exactly the same. Two fractions with different bottom numbers are easiest to compare once you scale one of them to match the other. ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Equivalent fractions on a number line](https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa) - [Equivalent fractions (age 8+)](https://lightmysky.com/learn/mathematics/equivalent-fractions-age-8-mt_FP-mjXaq3B) ## Opens up - [Adding fractions (different denominators)](https://lightmysky.com/learn/mathematics/adding-fractions-different-denominators-mt_-V7EnqU7gG) - [Simplifying Fractions](https://lightmysky.com/learn/mathematics/simplifying-fractions-mt_b7T-CjOYUR) - [Reasoning with Equivalences](https://lightmysky.com/learn/mathematics/reasoning-with-equivalences-mt_jCy07DyBNU) - [Converting tenths to hundredths](https://lightmysky.com/learn/mathematics/converting-tenths-to-hundredths-mt_NaqEP8xDhZ) - [Comparing fractions (age 9+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-9-mt_SXbZ3bC9z7) - [Multiplication as scaling](https://lightmysky.com/learn/mathematics/multiplication-as-scaling-mt_VKW8lOcFaw)