# Division

*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*,

*b*is nonzero, then

*a*=*c*÷*b*

*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.

The meaning of division by zero is not usually defined.

Table of contents |

2 Division of rational numbers 3 Division of real numbers 4 Division of complex numbers 5 Division in abstract algebra 6 External links |

## Division of integers

- 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 . This is the approach usually taken in mathematics.
- Give the answer as a
*quotient*and a*remainder*, so 26 ÷ 10 = 2 remainder 6. This approach is often used in computer science. 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.

## Division of rational numbers

The result of dividing two rational numbers is another rational number when the divisor is not 0. We may define division of two rational numbers *p*/*q* and *r*/*s* by

*p*may be 0. This definition ensures that division is the inverse operation of multiplication.

## Division of real numbers

## Division of complex numbers

All four quantities are real numbers.*r*and

*s*may not both be 0.

Division for complex numbers expressed in polar form is simpler and easier to remember than the definition above:

*r*may not be 0.

## Division in abstract algebra

is typically defined as or in abstract algebra like matrix algebra and quaternion algebra.

## 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, Vinculum