Division (mathematics) - Notation

Notation

Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a vinculum or fraction bar, between them. For example, a divided by b is written

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

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

A typographical variation halfway between these two forms uses a solidus (fraction 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), and there is no implication that the division must be evaluated further. A second way to show division is to use the obelus (or division sign), common in arithmetic, in this manner:

This form is infrequent except in elementary arithmetic. ISO 80000-2-9.6 states it should not be used. 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").

In elementary mathematics the notation or is used to denote a divided by b. This notation was first introduced by Michael Stifel in Arithmetica integra, published in 1544.