Question

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

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

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

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+y)+z+r=x(y+z)+r
left parenthesis x plus y right parenthesis plus z plus r equals x left parenthesis y plus z right parenthesis

Answer 1

The Associative Property of Addition states that the way in which numbers are grouped when added does not change their sum. In mathematical terms, this property can be expressed as:

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

Now, let's evaluate the options you provided to see which one demonstrates the Associative Property of Addition correctly:

1. **m⋅(x⋅y)=(m⋅x)⋅y**
This demonstrates the Associative Property of Multiplication, not Addition.

2. **y−(x+1)=(y−x)+1**
This is not relevant to the Associative Property of Addition; it describes a manipulation involving subtraction.

3. **x⋅(y+z)=(x⋅y)+z**
This demonstrates the Associative Property of Multiplication, not Addition.

4. **(x+y)+z+r=x(y+z)+r**
This expression is not valid as it mixes addition and multiplication without adhering to the Associative Property of Addition.

None of the options correctly demonstrate the Associative Property of Addition. The correct demonstration would be something like:

\((a + b) + c = a + (b + c)\) for any numbers \(a\), \(b\), and \(c\).