Which of the following correctly demonstrates the Associative Property of Addition?(1 point)

Question

Responses

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

y−(x+1)=(y−x)+1

Answer 1

The Associative Property of Addition states that the way numbers are grouped in an addition operation does not change their sum. This is expressed mathematically as:

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

Looking at the options provided:

1. m⋅(x⋅y)=(m⋅x)⋅y
   This represents the Associative Property of Multiplication.

2. (x+y)+z+r=x+(y+z)+r
   This correctly demonstrates the Associative Property of Addition.

3. x⋅(y+z)=(x⋅y)+z
   This does not represent the Associative Property (it's a mix of multiplication with addition).

4. y−(x+1)=(y−x)+1
   This does not demonstrate the Associative Property of Addition.

Therefore, the correct response is:

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