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
The lesson
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.
Watch it
Where it sits
8 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.