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This article is about the arithmetic operation. For other uses, see Division (disambiguation).
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 is not closed; apart from division by zero being undefined, the quotient will not be an integer unless
the dividend is an integer multiple of the divisor; for example 26 cannot be divided by 10 to give an integer. In such a case
there are three possible approaches.
- Say that 26 cannot be divided by 10.
- Give the answer as a decimal fraction or a mixed number, so 26 ÷ 10 = 2.6 or .
- Give the answer as a quotient and a remainder, so 26 ÷ 10 = 2 remainder 6. In some computer integer
arithmetic, 26/10 (or 26i / 10i) is given as 2 while 26 modulo 10 (or 26i % 10i) is given as 6.
is typically defined as or in abstract algebra like matrix algebra and quaternion algebra.
Left vs right, definition of quasigroup, relationship to inverse elements in presence of associativity, examples: groups,
octonions
External Links
Printable Worksheets for
Practicing Division
See also: Rational number, Vulgar fraction, Reciprocal, Inverse element, Divisor,
Division by two, Division by zero, Quasigroup, Group, Field (algebra), Division algebra, Division ring, Long
division
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