An Additive Inverse and its Operations in Math

ElevatEd
Math
March 21, 2025

An additive inverse is a tool that is mainly added to the originally given number to get a sum of zero. It is basically the opposite of the number. Additive inverse operations in Math work as negations of numbers or changes in the sign of the real number. Additive inverse helps solve equations in algebra by simplifying the equation.

The additive inverse of any number can be found by changing the sign of it. It works like the opposite form of the given number. If the number is positive it works with a negative additive inverse and the negative number works with a positive inverse. However, the numerical value will not change, only the sign will change. This piece of writing will discuss the additive inverse, its properties, and operations in math.

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Definition of Additive inverse with examples

An additive inverse is a value that is added to the original number and results in a zero value. It simply refers to changing the signs of the numbers and adding them to the original number to get a sum of zero. The positive number adds a negative inverse, and the negative number adds a positive inverse. The additive inverse is equivalent to the original number.

The formula of the additive inverse:

X = -X

Example:

The additive inverse of 4 is -4,

4+(-4) = 0

The additive inverse of 10 is -10

10+(-10) = 0

Additive inverse operations in maths

The main operation of additive inverse in Math refers to finding and working with the opposite number so that the sum of the number results in Zero.

The additive inverse is added to the given number, the result will be zero.

The positive number is added with the negative inverse and the negative number is added with the positive inverse.

Additive inverse helps in solving linear equations.

It can be used in a vector space and adding them results in the zero vector.

It is used in matrices, and the sum gives the zero matrix.

Additive inverse used in modular arithmetic.

Additive number operation with different numbers

The original number value can be a natural number, complex number or rational number.

The natural numbers are always positive so the additive inverse will be negative.

Example: 2+(-2) =0

The complex numbers are the mixture of real numbers and imaginary numbers.

Example: 4+5x+[-(4+5x)] = 4+5x-4-5x = 0

The rational numbers additive inverse will be the same number with a negative sign.

Example: (2/3) + (-2/3) = 0

In short, the concept of additive inverse in Math is a tool for solving equations. It is the exact opposite of the original number, while these numbers are added together the sum will be zero. The principle of additive inverse is not only applied to numbers but also to matrices, vectors, and modular arithmetic. This technique helps in solving mathematical equations and works as problem problem-solving technique. To know more about different mathematical aspects, visit www.98thpercentile.com or you can try our 1-week free trial classes on Math program.