Which property demonstrates that (a+b)+c is the same as a+(b+c)?

The correct answer is the Associative property, which specifically addresses the grouping of numbers in addition or multiplication without changing the result. According to the Associative property, when adding three or more numbers, the way in which the numbers are grouped does not change their sum.

For your example, (a+b)+c means you first add a and b together and then add c to that sum. Conversely, a+(b+c) means you first add b and c together and then add a to that result. In both cases, regardless of how the numbers are grouped, the final result remains the same. This property highlights that addition is flexible in terms of grouping, thereby solidifying its validity under this property.

The other options represent different mathematical properties. The Commutative property involves the rearrangement of numbers (e.g., a+b = b+a), the Distributive property relates to distributing a multiplier across terms (e.g., a(b+c) = ab + ac), and the Identity property states that adding zero to any number does not change its value (e.g., a + 0 = a). Understanding these properties helps in grasping fundamental concepts in mathematics.