Division (mathematics)

If ${\displaystyle c}$ times ${\displaystyle b}$ equals ${\displaystyle a}$, written as:

${\displaystyle c\cdot b=a}$

where ${\displaystyle b}$ is not zero, then ${\displaystyle a}$ divided by ${\displaystyle b}$ equals ${\displaystyle c}$, written as:

${\displaystyle {\frac {a}{b}}=c}$[2]

For instance,

${\displaystyle {\frac {6}{3}}=2}$

since

${\displaystyle 2\cdot 3=6}$.

In the above expression, ${\displaystyle a}$ is called the dividend, ${\displaystyle b}$ the divisor and ${\displaystyle c}$ the quotient.[2]

Division by zero, as in

${\displaystyle {\frac {x}{0}}}$

is not defined.

Division is most often shown by placing the dividend over the divisor with a horizontal line, also called a vinculum, between them. For example, ${\displaystyle a}$ divided by ${\displaystyle b}$ is written as

${\displaystyle {\frac {a}{b}}}$

This can be read as "a divided by b", or "a over b". A way to express division all on one line is to write the dividend, then a slash, then the divisor, like this:

${\displaystyle a/b}$

This is the usual way to specify division in most computer programming languages, since it can easily be typed as a simple sequence of characters.

A typographical variation which is halfway between these two forms uses a slash, but elevates the dividend and lowers the divisor:

^a⁄_b

Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers (in which case, the two numbers are typically referred to as numerator and denominator). A fraction is an accepted way of writing numbers. It is not always expected that the result of the division is written in decimals.

In some non-English-speaking cultures, "a divided by b" is written as ${\displaystyle a:b}$. However, in English-speaking countries the colon is restricted to expressing the related concept of ratios (where ${\displaystyle a:b}$ reads "a is to b").

• Divisor, another meaning as a number which evenly divides an amount
• Division by two
• Long division
• Modular arithmetic
• Remainder

1. "Division". www.mathsisfun.com. Retrieved 2020-08-26.
2. Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.

• Division on a Japanese abacus selected from Abacus: Mystery of the Bead
• Chinese Short Division Techniques on a Suan Pan
• Rules of divisibility Archived 2015-05-03 at the Wayback Machine