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

The Associative Property of Addition states that the way in which numbers are grouped in addition does not change their sum. In other words, for any numbers \(a\), \(b\), and \(c\), the equation \((a + b) + c = a + (b + c)\) holds true.

Among the options provided:

A: \(y - (x + 1) = (y - x) + 1\) - This does not demonstrate the Associative Property of Addition; it is a subtraction statement.

B: \((x + y) + z + r = x + (y + z) + r\) - This correctly demonstrates the Associative Property of Addition with respect to the terms \(x\), \(y\), and \(z\).

C: \(x * (y + z) = (x * y) + z\) - This illustrates a property related to multiplication and does not demonstrate the Associative Property of Addition.

D: \(m * (x * y) = (m * x) * y\) - This illustrates the Associative Property of Multiplication, not addition.

Therefore, the correct answer is:

**B: (x + y) + z + r = x + (y + z) + r**