Question

Mark wrote the highest score he made on his new video game as the product 70×6,000. Use the Associative and Commutative Properties to show how Mark can calcuate this product mentally.

Answer 1

The correct answer is:

We can use the associative property to write 70 as 7*10. We can do this same process to write 6000 as 6*1000. This gives us:

(7*10)*(6*1000)

Using the commutative property, we can rearrange the factors of this problem

(7*6)*(10*1000)

7*6 is in our multiplication tables, and we know that powers of 10 allow us to just add the correct number of zeros. This means we would have 7*6=42, and have 4 zeros, for 420000.

Answer 2

Associative:
70*6000 => (7*6) * (10*1000) =>
(42)*(10000) = 420000

Commutative:
(7*10) * (6*10*10*10) =>
7*6*10*10*10*10 => 42*10*10*10*10 =>
... => 420000