The additive inverse of a number, a is -a so that a+a=0
Associative or Commutative?
The property being referred to in this question is commutativity.
To determine whether a property is associative or commutative, we need to understand their definitions:
- Commutativity: The commutative property states that the order of the numbers or variables being combined does not affect the result. In other words, the operation can be performed in any order without changing the outcome.
- Associativity: The associative property states that the way numbers or variables are grouped when combined does not affect the result. In other words, the grouping of the numbers can be changed using parentheses without changing the outcome.
Now, let's analyze the given statement: "The additive inverse of a number, a, is -a so that a+a=0."
In this case, we are dealing with the addition operation. The statement tells us that the additive inverse of a number is obtained by replacing it with its negative counterpart. The equation "a + a = 0" is used to represent this relationship, where 0 is the additive identity.
Based on this information, we can conclude that the statement is an example of the commutative property of addition because it states that adding a number with its additive inverse results in zero, regardless of the order in which the numbers are added.