--- title: "Using inverse operations" description: "Recognise inverse relationships between operations and use them to check answers and simplify calculations." canonical: https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ source: https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ.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`. # Using inverse operations Recognise inverse relationships between operations and use them to check answers and simplify calculations. Subject: Mathematics · Area: Multiplication & Division · Ages 11 to 12 Page: https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ ## Ready when they can - Use addition and subtraction as inverse operations to check and solve problems - Use multiplication and division as inverse operations to check and solve problems - Recognise that squaring and square-rooting are inverse operations ## Lesson: Using inverse operations An inverse operation undoes another operation. Subtraction undoes addition, division undoes multiplication, and square-rooting undoes squaring. If you know one fact, the inverse gives you another fact. *(drawing: 7 rows of 6 make 42. Split 42 back into 7 rows and you get 6 in each row again. Multiplication and division are the same fact, run in two directions.)* **Example.** Zara works out 90 ÷ 9 = 10. She checks with the inverse, 10 × 9, which gives 90 and confirms her answer. The same trick works with addition and subtraction. If 156 + 27 = 183, you can check it with the inverse: 183 - 27. That should bring you straight back to 156. **Tip.** Squaring and square-rooting are inverses too: 8² = 64, and √64 = 8. After a calculation, ask which inverse operation can check it. This is often faster than doing the whole calculation again. **Recap.** Every operation has an inverse that undoes it, so use the inverse to check your answer instead of starting over. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Order of operations](https://lightmysky.com/learn/mathematics/order-of-operations-mt_jHgRQ4hR0g) - [Multi-step problems: choosing operations](https://lightmysky.com/learn/mathematics/multi-step-problems-choosing-operations-mt_RXnyhCRYXA) ## Opens up - [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU) - [Solving linear equations](https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO)