Question

Which of the following correctly demonstrates the Associative Property of Addition?(1 point) Responses x\cdot(y+z)=(x\cdot y)+z x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z m\cdot(x\cdot y)=(m\cdot x)\cdot y m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y y-(x+1)=(y-x)+1 y minus left parenthesis x plus 1 right parenthesis equals left parenthesis y minus x right parenthesis plus 1 (x+y)+z+r=x+(y+z)+r

Answer 1

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

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

From the options you've provided, the correct demonstration of the Associative Property of Addition is:

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

However, this exact expression does not appear in the options you have listed. But the equivalent expression you provided:

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

is a correct demonstration of the Associative Property of Addition, since it adds another variable \(r\) but still maintains the associative property.

Therefore, the correct response demonstrating the Associative Property of Addition is:

(x+y)+z+r = x+(y+z)+r