# Difference between revisions of "Division"

In mathematics, division is an arithmetic operation which is the inverse of multiplication.

## Overview

Since division is the inverse of multiplication then $a/b=a\cdot\frac{1}{b}.$

### Definition

If $a=bc$ and $b\ne 0$, then $\frac{a}{b}=c$, where $a$ is the dividend, $b$ is the divisor, and $c$ is the quotient.

### Process

The most common division algorithm used is with long division, a process that divides parts of numbers. Long division "breaks" up the number to make division simpler.

      19
6)114
-6
54
-54
0


### Conventions

If the quotient is not a whole number, it is usually written in decimal form: $5\div2=2.5$. Sometimes, it is written with its remainder: $5\div2=2\text{, remainder }1$.

## Dividing Special Numbers

### Fractions

If you divide by a fraction, multiply the dividend by the divisor's reciprocal (Note: You will see a definition of a reciprocal if you go to the article Ordinary Multiplication).

For instance: $6 \div \tfrac34 = 6 \cdot \tfrac43 = 8.$

### Decimals

When dividing by decimals, multiply both sides by a power of 10 so the divisor is an integer.

For instance: $15 \div 2.5 = 150 \div 25 = 6.$

### One and Itself

Any number divided by one equals itself. Similarly, any number divided by itself equals one.

For instance: $1992 \div 1 = 1992$ and $1985 \div 1985 = 1.$

### Zero

Division by $0$ is undefined. Equations where any values are divided by $0$ will become undefined also.