Additive Inverse (Definition, Properties & Examples)

The additive inverse is the amount that is added to a given number to make the sum zero. For instance, the result is zero if we take the number 4 and add -4 to it. Consequently, -4 is the additive inverse of 4. In everyday life, we encounter circumstances when we can eliminate the value of a quantity by using its additive inverse.

What is Additive Inverse?

The opposite number is a number's additive inverse. The straightforward rule is to reverse the positive and negative numbers. As we are aware, 10 + (-10) = 0. As a result, -10 is the additive inverse of 10, and vice versa.

Properties of additive inverse

Each real number is referred to as the additive inverse of the other when the product of two real numbers is zero. X is a real number, hence we have X +(-X)=0. The additive inverses of X and -X are one another. Such as 1/3 Plus (-1/3) Equals 0. In this case, 1/3 is -1/3's additive inverse, and vice versa. This is an illustration of a fraction's additive inverse. Let V =q+df be the given complex number. Then its inverse is -V= -q +df. For example, -d-1=-(-d-1)=d+1.

Additive Inverse Formula

The number itself can be used to express the generic formula for the additive inverse of a number. When a number's positive and negative halves are combined together, they cancel each other out and result in a sum of zero. The supplied integer Z's negative must be located. Therefore, we must locate -1 x (Z).

Algebraic Expressions using Additive Inverse

It is possible to use the additive inverse property to algebraic expressions. The additive inverse of an algebraic expression is one that reduces the total number of terms to zero, according to the same rule as previously stated. The expression's inverse additive sign is -. The additive inverse of x3 + 2 is - (x3 + 2) = -x3 - 2.

For example, the additive inverse of 8x + 9y is -8x - 9y, making the sum of all the elements zero.