Question

If a, b, c are real numbers, then which one of the following shows associative property addition?

• A. a+b=b+a
• B. a+(b+c)=(a+b)+c
• C. a(b+c)=ab+ac
• D. None of the above

Answer 1

The Correct Option is B

Step 1: Recall the associative property of addition.

The associative property states that for any real numbers \( a \), \( b \), and \( c \):

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

Step 2: Match the property to the options.

• (1) \( a + b = b + a \): This represents the commutative property of addition, not the associative property.
• (2) \( a + (b + c) = (a + b) + c \): This is the associative property of addition.
• (3) \( a(b + c) = ab + ac \): This represents the distributive property, not the associative property.
• (4) None of the above: Incorrect, as option (2) matches the associative property.

Final Answer: The correct option is \( \mathbf{(2)} \).