## 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 = 36+3 =9 | 2 × 3 =6 6 ÷ 3 = 2 | 8÷ 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 ^{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.