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# Division

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.

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

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

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

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