Additive Inverse

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

NumberAdditive inverse
1-1
-22
3-3
½
-⅓
¾
√2-√2
-√3√3
√5-√5

Learn more

Inverse Operation

Inverse Functions

Directly and Inversely Proportional

Equivalent Fractions

Definitions Index

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