Which expression demonstrates the associative property for addition?

Which expression demonstrates the associative property for addition?

• A. 8+(4+2)=(8+4)+2
• B. a+b=b+a
• C. a×b=b×a
• D. (a+b)×c = a+(b×c)

Answer: (D)

Associative property for addition means you can regroup the addends without changing the sum, written as (a + b) + c = a + (b + c). Using 8, 4, and 2, the regrouped forms are 8 + (4 + 2) and (8 + 4) + 2. Compute: 4 + 2 = 6, so 8 + 6 = 14. On the other side, 8 + 4 = 12, and 12 + 2 = 14. Since both expressions give the same total, this demonstrates the associative nature of addition. The other options show different ideas: swapping order shows commutativity, multiplying when swapped also shows commutativity, and mixing operations as in (a + b) × c ≠ a + (b × c) isn’t a valid rule for combining addition and multiplication—the correct distributive form would be (a + b) × c = a × c + b × c.

Associative property for addition means you can regroup the addends without changing the sum, written as (a + b) + c = a + (b + c). Using 8, 4, and 2, the regrouped forms are 8 + (4 + 2) and (8 + 4) + 2. Compute: 4 + 2 = 6, so 8 + 6 = 14. On the other side, 8 + 4 = 12, and 12 + 2 = 14. Since both expressions give the same total, this demonstrates the associative nature of addition. The other options show different ideas: swapping order shows commutativity, multiplying when swapped also shows commutativity, and mixing operations as in (a + b) × c ≠ a + (b × c) isn’t a valid rule for combining addition and multiplication—the correct distributive form would be (a + b) × c = a × c + b × c.