Special rules that make multiplication easier — commutative, associative, and distributive!
Multiplication has three powerful properties: the Commutative Property (you can flip the factors), the Associative Property (you can regroup when multiplying three numbers), and the Distributive Property (you can break a factor apart to multiply in pieces).
3 × 5 = 15 and 5 × 3 = 15 The ORDER of the factors does not change the product! "Commute" means to move back and forth — the factors can swap places.
(2 × 3) × 4 = 6 × 4 = 24 2 × (3 × 4) = 2 × 12 = 24 No matter how you GROUP three factors, the product is the same!
6 × 7 = 6 × (5 + 2) = (6 × 5) + (6 × 2) = 30 + 12 = 42 Break a hard problem into two easy ones and ADD the results!
Remember This!
Use the Distributive Property to handle tricky facts. To find 8 × 7, think: (8 × 5) + (8 × 2) = 40 + 16 = 56.
Using the commutative property, if 9 × 6 = 54, what is 6 × 9?