Properties of Operations
Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Break numbers apart or group them differently. The answer always stays the same.
More to read
2.5: Properties of Multiplication
Three properties make multiplication friendly. Commutativity says order does not matter: 6 x 4 equals 4 x 6. Associativity says grouping does not matter. Distributivity lets you split a hard multiplication into easy parts.
Use these rules to reshape problems. Turning 8 x 7 into 8 x 5 + 8 x 2 swaps one hard fact for two easy ones.
Properties of multiplication
Multiplication follows friendly rules. You can swap the order, regroup the numbers, or split one factor apart, and the answer stays put. These rules are called properties.
Properties are tools, not trivia. Reach for them whenever a calculation looks awkward.
Commutative property of multiplication review
Swapping the order never changes a product. Three bags of 4 apples hold the same fruit as 4 bags of 3 apples. Both give 12.
This halves your memory work. Learn 7 x 8 and you get 8 x 7 free.
Explore more
2 · Watch
به انگلیسیTake it off screen
Where it sits
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.