Difference between revisions of "Division"
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| − | {{ | + | In [[mathematics]], '''division''' is an arithmetic [[operation]] which is the inverse of [[multiplication]]. |
| + | |||
| + | ==Overview== | ||
| + | Since division is the inverse of multiplication then <math>a/b=a\cdot\frac{1}{b}.</math> | ||
| − | |||
| − | == 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 [[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 === | ||
| + | Division by <math>0</math> is undefined. Equations where any values are divided by <math>0</math> will become undefined also. | ||
== See Also == | == See Also == | ||
Latest revision as of 08:52, 23 January 2020
In mathematics, division is an arithmetic operation which is the inverse of multiplication.
Contents
Overview
Since division is the inverse of multiplication then 
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.
19
6)114
-6
54
-54
0
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
Division by 
is undefined. Equations where any values are divided by will become undefined also.
