Additive Inverse Definition
It is a number that gives “0” as the answer when added to the original term or digit. Simply, Additive Inverse is the opposite term, number, or variable of the original term, number, or variable
Note:
You can read about Terms and Variables here.
Table of Contents
For Example:
- 5 is the additive inverse of -5 and vice versa.
- -x is the additive inverse of x and vice versa.
- 2y is the additive inverse of -2y and vice versa.
How to find the additive inverse of the given number?
You can find the additive inverse of any number or term within seconds. It is pretty simple because you only have to change the sign of the original term. You have to write the original term and then write the same term with opposite signs to get the additive inverse of the original term.
Example 1:
Find the Additive Inverse of -5.
Solution:
As the original term has a negative sign, we only need to change the sign of the given term.
= +5
To check if both numbers are the additive inverse of each other or not, we have to add them.
= -5 + (+5)
= 0
As it yields “0” as the output of the above addition, it means that these terms are the additive inverse of each other.
Term Related to Additive Inverse
In Mathematics, another term related to this is used. It is called Multiplicative Inverse. As the name shows, it defines the term that yields “1” as the result when the terms are multiplied by each other.
Note:
Read about Multiplicative Inverse here.
Difference between Additive and Multiplicative Inverse
- Additive Inverse yields “0” while Multiplicative Inverse yields “1”.
- In Additive Inverse, signs of the original term and a new one must be opposite. In Multiplicative Inverse, the signs can be the same for both terms.
- In Additive Inverse, the terms should be in the same format while the terms should be in the reciprocal format in Multiplicative Inverse.
Can we find the Additive Inverse of a Complex number
Yes, it is possible to find the additive inverse of any term or number including complex numbers. You only have to reverse the signs of the given complex term to get “0” as the resultant. It will show that the new term is the additive inverse of the original one because it is yielding “0” while added.
Note:
You can read about Complex Numbers here.
Example 2:
Find the additive inverse of 2x - 2i.
Solution:
To find the additive inverse, we only have to reverse their signs.
= -2x + 2i
As we can see that the above two terms will yield “0” on adding. It means that these terms are the additive inverse of each other.
Fun Facts about Additive Inverse
- 0 has no additive inverse.
- Two integers with the same quantity and opposite signs are the additive inverse of each other.
- Two terms should be in the same format to be additive inverse. .
- An additive inverse can be found by multiplying “-1” with the original term.
FAQ's
How to find the Additive Inverse of the given number?
We can find the additive inverse of the given number by multiplying it with “-1”.
Does 0 have an additive inverse?
No, 0 has no additive inverse.
What is the additive inverse of -7?
The additive inverse of -7 is +7.
What is the additive inverse of 2/3?
The additive inverse of 2/3 is -2/3 because it yields “0” on addition.
