Which statement demonstrates the concept of associativity?

Which statement demonstrates the concept of associativity?

• A. Commutativity
• B. Distributivity
• C. Identity
• D. Associativity

Answer: (D)

Associativity is the idea that the way you group operations doesn’t change the result. For a binary operation, you can put parentheses in different places and still get the same outcome, as long as the operation is the same. A simple example with addition shows this: (2 + 3) + 4 equals 9, and 2 + (3 + 4) also equals 9. This demonstrates the property that (a + b) + c = a + (b + c). The other options refer to different ideas: commutativity is about swapping the order of the operands, distributivity is about how multiplication distributes over addition, and identity is about a neutral element that leaves a value unchanged. So the statement that shows grouping can vary without changing the result is the one that truly demonstrates associativity.

Associativity is the idea that the way you group operations doesn’t change the result. For a binary operation, you can put parentheses in different places and still get the same outcome, as long as the operation is the same. A simple example with addition shows this: (2 + 3) + 4 equals 9, and 2 + (3 + 4) also equals 9. This demonstrates the property that (a + b) + c = a + (b + c). The other options refer to different ideas: commutativity is about swapping the order of the operands, distributivity is about how multiplication distributes over addition, and identity is about a neutral element that leaves a value unchanged. So the statement that shows grouping can vary without changing the result is the one that truly demonstrates associativity.