Question

Which strategy might Silvia use to compare the products of 50 x 225 and 25 x 225 without computing the solutions?

A) Use the associative property of multiplication.
B) Apply the distributive property of multiplication.
C) Employ mental estimation and rounding.
D) Utilize the commutative property of multiplication.

Answer 1

Silvia might use the associative property of multiplication to compare the products of 50 x 225 and 25 x 225, realizing that the second product is half the size of the first since 25 is half of 50.

Step-by-step explanation:

To compare the products of 50 x 225 and 25 x 225 without computing the solutions, Silvia might use the associative property of multiplication. This property states that you can change the grouping of the numbers in a multiplication problem and it will not affect the product. In this case, Silvia could group 50 with 225 as 50 x 225, and then she would observe that 25 is half of 50.

Noticing that 25 x 225 is the same as (50/2) x 225, Silvia can deduce that the second product 25 x 225 will be half the size of the first product 50 x 225 because she is effectively halving one of the factors. This understanding allows her to compare the two products quickly without manual calculation.