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
Operations |
Inverse operations |
Addition |
Subtraction |
Subtraction |
Addition |
Multiplication |
Division |
Division |
Multiplication |
Inverse operators
More examples of inverse operations
Operator |
+ |
_ |
× |
÷ |
Inverse operator |
_ |
+ |
÷ |
× |
Example |
5+4 = 9 5-4 =1 |
6-3 = 3 6+3 =9 |
2 × 3 =6 6 ÷ 3 = 2 |
8÷ 2 = 4 2 × 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 ^{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.