# Subtraction

*995*pages on

this wiki

In arithmetic and higher mathematics, **subtraction** is the inverse operation of addition.

In lower-level elementary mathematics and when using signed integers in programming languages, subtracting a number from a number with lower value is undefined.

## Subtraction in different fields

- Integer subtraction:
*a*-*b*is equivalent to*a*+*-b*, where -*b*is the additive inverse of*b*.- Example: 9 - 8 = 1

- Real number and complex number subtraction:
- Example: 8.2 - (5 + 2i) = 3.2 - 2i

- Matrix subtraction: A - B = A + -B

## Properties

- Generally, subtraction is
**not**commutative nor associative. - 3 - 6 ≠ 6 - 3
- But keep in mind that 6-3=3 and 3-6=negative3, so switching the subtrahend with the minuend gives the inverse difference.

## In real life.

Subtraction is used in real life like addition like in computing change, calculating the amount remaining from a bank account, and many others.

## Estimation

This can be done in the same way as addition.