Table of Contents
Definition of Additive Inverse
The additive inverse of a number is another number you add to a number to create the sum of zero. In other words, additive inverse of x is another number, for examle y, as long as the sum of x + y equals zero.
The additive inverse of x is equal and opposite in sign to it. If y is the additive inverse of x, then y = -x or vice versa. For example, the additive inverse of the positive number 4 is -4. That’s because their sum is zero, or 4 + (-4) = 0.
So, Additive Inverse of a number is the negative of that number.
Additive Inverse of a Negative Number
If x is a negative number, by using the same approach then its additive inverse is equal and opposite in sign to it. Which means that the additive inverse of a negative number is a positive number.
For example, if x equals -7, then its additive inverse is y = 7. Then verify that the sum of x + y equals zero, since x = -7 and y = 7, we have -7 + 7 = 0.
Note that the additive inverse of 0 is 0. 0 is the only real number, which is equal to its own additive inverse. Zero is also the only number for which the equation x = -x is true.
Additive Inverse is what number you add to a number to get zero.
Example:
- -7 is additive inverse of 7, because 7 + (-7) = 0
- 4 is additive inverse of -4, because -4 + 4 = 0
Table of additive inverse
| Number | Additive inverse |
| 1 | -1 |
| -2 | 2 |
| 3 | -3 |
| ½ | -½ |
| -⅓ | ⅓ |
| ¾ | -¾ |
| √2 | -√2 |
| -√3 | √3 |
| √5 | -√5 |