Inverse operations - Definition with Examples

Inverse Operations

Operation is a mathematical process involving addition, subtraction, multiplication, division, squaring, square roots, etc. 

All the given symbols (+, −, ×, ÷) in mathematics are known as operators. 

An inverse operation reverses the effect of the first operation. 

For example, if we operated adding two numbers say 5+3 = 8

The inverse operation of this would be the subtraction of these two numbers: 5-3= 2.

Inverse Operators 

The primary operations in mathematics are addition, subtraction, multiplication, and division.  The inverse operations of these are given in the table below:  

Inverse operations

Inverse operators 

More examples of inverse operations 

Properties of Inverse Operations

Inverse additive property: The inverse operation of the addition of two same numbers will result in a zero.

2 + (-2) = 0

or

When we add a number to its opposite, the result is always 0. 

Inverse multiplicative property: When we multiply a number is by its (multiplicative) inverse, the result is always 1. 

Multiplicative inverse of 10 is ¹⁄₁₀

So, 10 × ¹⁄₁₀=1

Additive Property: Consider the operation , 5 + 0 = 5 

The inverse operation is,  5-  0  = 5 

Thus, when we add any number to zero, both the operation and inverse operation will give the same number. 

Multiplicative Property: Consider the operation,  5 × 1 = 5

The inverse operation is, 5 ÷ 1 = 5 

Thus, when we multiply any number with 1, both the operation and inverse operation will give the same number.