--- title: "Properties of Operations" description: "Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide" canonical: https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR source: https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR.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`. # Properties of Operations Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide Subject: Mathematics · Area: Multiplication & Division · Ages 8 to 9 Page: https://lightmysky.com/learn/mathematics/properties-of-operations-mt_Lb2ZnMdkYR ## Ready when they can - Use commutativity: if 6 × 4 = 24 then 4 × 6 = 24 - Use the distributive property: 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56 - Use associativity to multiply three numbers: 2 × 3 × 5 = 6 × 5 = 30 ## Lesson: Breaking numbers apart to multiply You already know a multiplication fact can flip around: if 6 × 4 = 24, then 4 × 6 = 24 too. Today you will learn two more tricks. You can break a number into smaller pieces, or group numbers in a new order. Both tricks give the same answer, just an easier path to it. *(drawing: Picture 8 rows of 7. Split the 7 into 5 and 2. Now 8 × 5 = 40 and 8 × 2 = 16. Add them: 40 + 16 = 56. This is the distributive property: break one number apart, multiply each piece, then add.)* **Example.** Mia wants to multiply 6 × 14 in her head. She breaks 14 into 10 and 4. Then 6 × 10 = 60 and 6 × 4 = 24. She adds 60 + 24 = 84. **Tip.** When you multiply three numbers, like 2 × 3 × 5, you can multiply any two first. Try 2 × 3 = 6, then 6 × 5 = 30. Or try 3 × 5 = 15, then 2 × 15 = 30. Either way, you get 30. This is the associative property: grouping numbers differently never changes the answer. **Recap.** Break numbers apart or group them differently. The answer always stays the same. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Commutative Multiplication](https://lightmysky.com/learn/mathematics/commutative-multiplication-mt_C9ZfT-4cgn) - [What Multiplication Means](https://lightmysky.com/learn/mathematics/what-multiplication-means-mt_gtTl3R5buH) ## Opens up - [Multiply & Add Problems](https://lightmysky.com/learn/mathematics/multiply-and-add-problems-mt_AR-K72OIIO) - [Factor Pairs & Commutativity](https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX) - [Mental multiplication and division](https://lightmysky.com/learn/mathematics/mental-multiplication-and-division-mt_pjfmCMMPjO) - [Patterns in addition and multiplication tables](https://lightmysky.com/learn/mathematics/patterns-in-addition-and-multiplication-tables-mt_w6MxaaoMXZ)