Sum of integers and its additive inverse
Integers are whole numbers, both positive and negative, along with zero. When we talk about the sum of an integer and its additive inverse, we are essentially looking at the result when we add a number to its negative counterpart.

Definition of additive inverse
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. For example, the additive inverse of 5 is -5 because 5 + (-5) = 0.

Sum of an integer and its additive inverse
When we add an integer to its additive inverse, the result is always zero. This is a fundamental property of integers. For any integer 'a', its additive inverse is '-a'. Therefore, the sum of 'a' and '-a' is always zero.

Example
Let's take an example to illustrate this concept. If we have the integer 7, its additive inverse is -7. When we add 7 and -7, we get:
7 + (-7) = 0

Significance
Understanding the concept of additive inverses is crucial in the study of integers. It helps in performing operations like addition and subtraction with ease. The sum of an integer and its additive inverse being zero is a key property that simplifies calculations involving integers.
In conclusion, the sum of an integer and its additive inverse is always zero, highlighting the symmetry and balance in the world of integers.

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