What kind of property is demonstrated by the equation (a+b)+c = a+(b+c)?

The equation (a+b)+c = a+(b+c) exemplifies the Associative Property. This property addresses how numbers are grouped in addition or multiplication without affecting the outcome. It highlights that when adding or multiplying three or more numbers, the way in which the numbers are grouped does not change the result.

For instance, in the given equation, whether you first add a and b, and then add c, or first add b and c, and then add a, the total will be the same. This property is foundational in arithmetic and algebra as it assures that calculation order can vary without altering the final sum, allowing for flexibility in solving expressions.

In contrast, the Commutative Property refers to the idea that changing the order of the numbers does not affect the sum or product (e.g., a+b = b+a). The Distributive Property involves distributing a multiplication over addition, such as a(b+c)=ab+ac. The Identitative Property, while less commonly referenced, generally involves how certain identities behave under operations, but it is not directly related to grouping in addition. Hence, the correct identification of the property described in the equation is the Associative Property.