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

Question

• (x + y) + 2 + 7 = x + (y + z) + r
0 т . (х • у) = (т. х) • у
• y - (x + 1) = (y -x) + 1
0 x • (y + z) = x • y) + z

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 the sum. In mathematical terms, this property can be expressed as:

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

Let's evaluate the options given to find the one that correctly demonstrates this property:

1. (x + y) + 2 + 7 = x + (y + z) + r
   This does not demonstrate the associative property as the right side does not match the left in structure.

2. 0 т . (х • у) = (т. х) • у
   This describes the Associative Property of Multiplication, not Addition.

3. y - (x + 1) = (y - x) + 1
   This expression illustrates a subtraction operation, not addition.

4. 0 x • (y + z) = (x • y) + z
   This again describes multiplication rather than addition.

Based on the listed options, none correctly demonstrate the Associative Property of Addition. The correct demonstration would involve an expression that maintains the property \( (a + b) + c = a + (b + c) \).