Division

This article is about the arithmetic operation. For other uses, see Division (disambiguation).

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In mathematics, especially elementary arithmetic, division is an arithmetic operation which is the reverse operation of multiplication and sometimes can be interpreted as repeated subtraction.

Specifically, if

a × b = c,

where b is nonzero, then

a = c ÷ b

(read as "c divided by b"). So for instance, 6 ÷ 3 = 2 since 2 × 3 = 6.

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

The expression c ÷ b is also written "c/b" (read "c over b"), especially in higher mathematics (including applications to science and engineering) and in computer programming languages. This form is also often used as the final form of a fraction, without any implication that it needs to be evaluated further.

It is not possible to define division by zero in any useful way.

Division of integers

Explain how we get both a quotient and a remainder, link to Modular arithmetic

Division in abstract algebra

Left vs right, definition of quasigroup, relationship to inverse elements in presence of associativity, examples: groups, octonions

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See also: Rational number, Reciprocal, Inverse element, Divisor, Division by two, Division by zero, Quasigroup, Group, Field (algebra), Division algebra, Division ring, Long division[?]