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

Question

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

x⋅(y+z)=(x⋅y)+z

y−(x+1)=(y−x)+1

m⋅(x⋅y)=(m⋅x)⋅y

Answer 1

The Associative Property of Addition states that when three or more numbers are added, the way in which the numbers are grouped does not change the sum. This means that changing the parentheses does not affect the result.

From the options provided, the one that correctly demonstrates the Associative Property of Addition is:

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

This shows that the sum remains the same regardless of how the numbers are grouped.

The other options represent different properties:

• \(x \cdot (y+z) = (x \cdot y) + z\) demonstrates the Distributive Property.
• \(y - (x + 1) = (y - x) + 1\) does not represent an associative property and is not a standard algebraic law.
• \(m \cdot (x \cdot y) = (m \cdot x) \cdot y\) demonstrates the Associative Property of Multiplication, not addition.

Thus, the correct answer is:

\((x+y)+z+r=x+(y+z)+r\) (Associative Property of Addition).

Answer 2

is it A?

Answer 3

Yes, you are correct; the option you are referring to as option A is indeed the one that demonstrates the Associative Property of Addition. Specifically,

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

is the correct demonstration of this property.

The other options do not represent the Associative Property of Addition. Thank you for your clarification!