# Difference between revisions of "Division"

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− | + | In [[mathematics]], '''division''' is an arithmetic [[operation]] which is the inverse of [[multiplication]]. | |

− | + | ==Overview== | |

− | == Definition == | + | === Definition === |

If <math>a=bc</math> and <math>b\ne 0</math>, then <math>\frac{a}{b}=c</math>, where <math>a</math> is the [[dividend]], <math>b</math> is the [[divisor]], and <math>c</math> is the [[quotient]]. | If <math>a=bc</math> and <math>b\ne 0</math>, then <math>\frac{a}{b}=c</math>, where <math>a</math> is the [[dividend]], <math>b</math> is the [[divisor]], and <math>c</math> is the [[quotient]]. | ||

− | == Conventions == | + | === 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. | ||

+ | |||

+ | <u> 19</u> | ||

+ | 6)114 | ||

+ | <u>-6</u> | ||

+ | <span>5</span>4 | ||

+ | <u>-54</u> | ||

+ | 0 | ||

+ | |||

+ | |||

+ | |||

+ | ===Conventions=== | ||

If the quotient is not a [[whole number]], it is usually written in decimal form: <math>5\div2=2.5</math>. Sometimes, it is written with its [[remainder]]: <math>5\div2=2\text{, remainder }1</math>. | If the quotient is not a [[whole number]], it is usually written in decimal form: <math>5\div2=2.5</math>. Sometimes, it is written with its [[remainder]]: <math>5\div2=2\text{, remainder }1</math>. | ||

− | == Dividing | + | == Dividing Special Numbers== |

− | 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]]. | + | |

+ | === 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: <math>6 \div \tfrac34 = 6 \cdot \tfrac43 = 8.</math> | ||

+ | |||

+ | === Decimals === | ||

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

+ | |||

+ | For instance: <math>15 \div 2.5 = 150 \div 25 = 6.</math> | ||

+ | |||

+ | === One and Itself === | ||

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

+ | |||

+ | For instance: <math>1992 \div 1 = 1992</math> and <math>1985 \div 1985 = 1.</math> | ||

− | == | + | === Zero === |

You CANNOT divide by 0! | You CANNOT divide by 0! | ||

## Revision as of 13:49, 11 August 2018

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

## Contents

## Overview

### Definition

If and , then , where is the dividend, is the divisor, and 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.

196)114-654-540

### Conventions

If the quotient is not a whole number, it is usually written in decimal form: . Sometimes, it is written with its remainder: .

## 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:

### Decimals

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

For instance:

### One and Itself

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

For instance: and

### Zero

You CANNOT divide by 0!