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# Division

In mathematics **division** is an operation which is the opposite of multiplication.

If *c* times *b* equals *a*, written:

- [math]\displaystyle{ c \times b = a }[/math]

where *b* is not zero, then *a* divided by *b* equals *c*, written:

- [math]\displaystyle{ \frac ab = c }[/math]

For instance,

- [math]\displaystyle{ \frac 63 = 2 }[/math]

since

- [math]\displaystyle{ 2 \times 3 = 6 }[/math].

In the above expression, *a* is called the **dividend**, *b* the **divisor** and *c* the **quotient**.

Division by zero

- [math]\displaystyle{ \frac x0 =? }[/math]

...is not defined.

## Notation

Division is most often shown by placing the *dividend* over the *divisor* with a horizontal line, also called a vinculum, between them. For example, *a* divided by *b* is written

- [math]\displaystyle{ \frac ab }[/math].

This can be read out loud 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:

- [math]\displaystyle{ a/b.\, }[/math]

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 (although typically called the *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.

A less common way to show division is to use the obelus (or division sign) in this manner:

- [math]\displaystyle{ a \div b. }[/math]

But in elementary arithmetic this form is used rather often. The obelus is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.

In some non-English-speaking cultures, "a divided by b" is written *a* : *b*. However, in English usage the colon is restricted to expressing the related concept of ratios (then "a is to b").

## Other pages

Adapted from Simple English Wikipedia