Which of the following correctly demonstrates the Associative Property of Addition? Responses m⋅(x⋅y)=(m⋅x)⋅y m⋅(x⋅y)=(m⋅x)⋅y - no response given (x+y)+z+r=x+(y+z)+r open paren x plus y close paren plus z plus r is equal to x plus open paren y plus z close paren plus r - no response given x⋅(y+z)=(x⋅y)+z x⋅(y+z)=(x⋅y)+z - no response given y−(x+1)=(y−x)+1

Answer 1

The Associative Property of Addition states that the way in which numbers are grouped in an addition problem does not change the sum. In algebraic terms, this can be expressed as:

\[ (a + b) + c = a + (b + c) \]

Among the options provided, the one that demonstrates the Associative Property of Addition is:

\[ (x + y) + z + r = x + (y + z) + r \]

This correctly shows that when adding multiple numbers, the grouping does not affect the result.

The other options given do not represent the Associative Property of Addition and therefore are not correct examples.