Describe two different ways that you could find the product 8 x 997 using mental math. find the product and explain why your method works.

We want to find 8 x 997 using mental math.

Method 1:
8 x 997 = 8*(1000 - 3)
              = 8*1000 - 8*3
              = 8000 - 24
              = 7976

Method 2
8 x 997 = (10 - 2)*997
              = 9970 - 2*997
              = 9970 - 1994
              = 7976

The two methods work because they use the associative and commutative properties of manipulating numbers and algebraic expressions.