Inverse Operations – Definition with Examples

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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 Operations

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

OperationsInverse operations
AdditionSubtraction
SubtractionAddition
MultiplicationDivision
DivisionMultiplication

Inverse operators 

Inverse operation

More examples of inverse operations 

Operator+           _×÷
Inverse operator          _ +÷×
Example 5+4 = 9 5-4 =1 6-3 = 36+3 =92 × 3 =6 6 ÷ 3 = 28÷ 2 = 42 × 4 = 8

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 110

So, 10 × 110=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. 


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