Question

Which expression requires you to use the Associative Property of Addition in order to simplify?

A. [y + (-y)] + x
B. y + (x + (-x)]
C. (y + x) + (-x)
D. y + (-x + x)

Answer 1

Option C, (y + x) + (-x), requires the use of the Associative Property of Addition to simplify the expression, allowing x + (-x) to cancel each other out.

Step-by-step explanation:

The question asks which expression requires the use of the Associative Property of Addition to simplify it. The Associative Property of Addition states that the grouping of numbers does not affect their sum, i.e., (A + B) + C = A + (B + C). Let's analyze the given options:

• A. [y + (-y)] + x
• B. y + (x + (-x))
• C. (y + x) + (-x)
• D. y + (-x + x)

The expression that requires the use of the Associative Property of Addition in order to be simplified is option C: (y + x) + (-x). Using the Associative Property, we can re-group the numbers as y + (x + (-x)) which simplifies further to y + 0, as x and (-x) cancel each other out, resulting in just y.