Which of the following correctly demonstrates the Associative Property of Addition?(1 point)
Responses
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
m⋅(x⋅y)=(m⋅x)⋅y
m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y
(x+y)+z+r=x+(y+z)+r
left parenthesis x plus y right parenthesis plus z plus r equals x plus left parenthesis y plus z right parenthesis plus r
x⋅(y+z)=(x⋅y)+z
x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z
x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z
The correct equation that demonstrates the Associative Property of Addition is:
(x+y)+z+r = x+(y+z)+r
To understand why this equation represents the Associative Property of Addition, let's first understand what the property means. The Associative Property of Addition states that you can change the grouping of numbers being added without changing the result.
In the given equation, we have four numbers: x, y, z, and r. According to the Associative Property of Addition, we can group them differently and still get the same result.
On the left side of the equation, we have (x+y)+z+r. This means we first add x and y, and then add the result to z, and finally add r to the previous sum.
On the right side of the equation, we have x+(y+z)+r. Now, we first add y and z, and then add the result to x, and finally add r to the previous sum.
Both sides of the equation represent the same mathematical operation but with different groupings, which is allowed by the Associative Property of Addition. Therefore, (x+y)+z+r = x+(y+z)+r demonstrates the Associative Property of Addition.