Which of the following correctly demonstrates the Associative Property of Addition?

Question

A. m*(x*y)=(m*x)*y
B. y-(x+1)=(y-x)+1
C. x*(y+z)=(x+y)+z
D. (x+y)+z+r=x+(y+z)+r

Answer 1

The Associative Property of Addition states that when adding three or more numbers, the way in which the numbers are grouped does not change their sum.

Among the options given:

A. \( m*(xy)=(mx)*y \) - This demonstrates the Associative Property of Multiplication, not Addition.

B. \( y-(x+1)=(y-x)+1 \) - This is not related to the Associative Property of Addition.

C. \( x*(y+z)=(x+y)+z \) - This demonstrates the Associative Property of Multiplication, not Addition.

D. \( (x+y)+z+r=x+(y+z)+r \) - This correctly demonstrates the Associative Property of Addition. It shows that whether you group \( (x+y) \) or \( (y+z) \), you still get the same result when adding all the elements.

Thus, the correct answer is:

D. \( (x+y)+z+r=x+(y+z)+r \)