Difference between revisions of "Division"

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In [[mathematics]], '''division''' is an arithmetic [[operation]] which is the inverse of [[multiplication]].
  
In [[mathematics]], '''division''' is an arithmetic [[operation]] which is the inverse of [[multiplication]].
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==Overview==
  
== Definition ==
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=== 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 ==
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=== 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.
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 +
    <u>  19</u>
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    6)114
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      <u>-6</u>
 +
      <span>5</span>4     
 +
      <u>-54</u>
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        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 by fractions ==
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== 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]].
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 +
=== 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 ===
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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 ===
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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>
  
== Dividing by 0 ==
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=== 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.

Overview

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

You CANNOT divide by 0!

See Also

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