Which equation shows the associative property of addition?

Which equation shows the associative property of addition?

• A. (A + B) + C = A + (B + C)
• B. A + (B + C) = (A + B) + C
• C. A + B = B + A
• D. A + 0 = A

Answer: (A)

The idea being tested is that when you add three numbers, the way you group them doesn’t change the sum. For example, with numbers 2, 3, and 4, (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. This shows that the grouping can change, but the total stays the same. The equation that shows this idea is the one where the two ways of grouping are placed on either side of the equals sign: (A + B) + C = A + (B + C). This clearly demonstrates that whatever way you parenthesize the additions, the result is the same. The other forms illustrate different properties. A + B = B + A is about commutativity—changing the order of the addends. A + 0 = A shows the additive identity—adding zero doesn’t change the value. The main statement of associativity uses the grouped form on both sides to highlight how grouping affects the operation, which is why this form is the best representation.

The idea being tested is that when you add three numbers, the way you group them doesn’t change the sum. For example, with numbers 2, 3, and 4, (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. This shows that the grouping can change, but the total stays the same.

The equation that shows this idea is the one where the two ways of grouping are placed on either side of the equals sign: (A + B) + C = A + (B + C). This clearly demonstrates that whatever way you parenthesize the additions, the result is the same.

The other forms illustrate different properties. A + B = B + A is about commutativity—changing the order of the addends. A + 0 = A shows the additive identity—adding zero doesn’t change the value. The main statement of associativity uses the grouped form on both sides to highlight how grouping affects the operation, which is why this form is the best representation.