Difference between revisions of "Division"

Latest revision as of 08:52, 23 January 2020

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.

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.

@@ Line 1: / Line 1: @@
 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 ===
 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]].
-Sometimes, the quotient will not be a [[whole number]]. In this case, it is usually written out in decimal form. For example, <math>\frac{3}{2}=1.5</math>. However, it may be necessary to write the [[remainder]]: <math>\frac{3}{2}=1</math> remainder 1.
+=== 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>
+)114
+      <u>-6</u>
+       <span>5</span>4
+      <u>-54</u>
+===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>.
+== 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: <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.
-When dividing by a fraction, it is easier to re-write the [[expression]] so that you are multiplying by the reciprocal of the fraction. For example, <math>4\div\frac{2}{3}=4\times\frac{3}{2}=6</math>.
+For instance: <math>1992 \div 1 = 1992</math> and <math>1985 \div 1985 = 1.</math>
-{{stub}}
+=== Zero ===
-{{wikify}}
+Division by <math>0</math> is undefined. Equations where any values are divided by <math>0</math> will become undefined also.
+== See Also ==
+* [[Addition]]
+* [[Subtraction]]
+* [[Multiplication]]
 [[Category:Definition]]
 [[Category:Operation]]

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