Which property explains why (A + B) + C equals A + (B + C)?

Which property explains why (A + B) + C equals A + (B + C)?

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

Answer: (A)

Associativity is the idea that how you group numbers during addition doesn’t change the final result. If you try a simple check with actual numbers: (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. Because addition behaves in this way, the two different ways of parenthesizing A, B, and C give the same answer, so (A + B) + C equals A + (B + C). Commutativity would be about reordering the terms (like swapping A and B) rather than changing how they’re grouped, so it doesn’t explain why the two parenthesizations yield the same result. Distributivity and idempotence involve other rules (like distributing over addition with multiplication or A + A = A), so they don’t account for this particular equality either.

Associativity is the idea that how you group numbers during addition doesn’t change the final result. If you try a simple check with actual numbers: (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. Because addition behaves in this way, the two different ways of parenthesizing A, B, and C give the same answer, so (A + B) + C equals A + (B + C).

Commutativity would be about reordering the terms (like swapping A and B) rather than changing how they’re grouped, so it doesn’t explain why the two parenthesizations yield the same result. Distributivity and idempotence involve other rules (like distributing over addition with multiplication or A + A = A), so they don’t account for this particular equality either.