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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 non zero, 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.

In most non- English languages, c ÷ b is written c : b. In English usage the colon is restricted to the related concept of ratios.

The meaning of division by zero is not usually defined.

1 Computing division

With a knowledge of multiplication tables, two integers can be divided on paper using the method of long divisionIn arithmetic, long division is an algorithm for division of two real numbers. It requires only the means to write the numbers down, and is simple to perform even for large dividends because the algorithm separates a complex division problem into smaller. If the dividend has a fractional part (expressed as a decimal fraction), one can continue the algorithm past the ones place as far as desired. If the divisor has a fractional part, one can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction.

Division can be calculated with an abacusSee also abacus (architecture) a flat slab at the top of a column. An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It was in use centuries before the adoption of the written Arabic numeral system and is st by repeatedly placing the dividend on the abacus, and then subtracting the divisor the offset of each digit in the result, counting the number of divisions possible at each offset.

In modular arithmeticModular arithmetic Group theory In mathematics, modular arithmetic is a system of arithmetic for certain equivalence classes of integers, called congruence classes . In modular arithmetic, numbers 'wrap around' after they reach a certain value (the modulu, some numbers have a multiplicative inverse with respect to the modulus. In such a case, division can be calculated by multiplication. This approach is useful in computers that do not have a fast division instruction.

2 Division of integerThe integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3,. and the number zero. The set of all integers is usually denoted in mathematics by Z (or Z in blackboard bold, ), which sts

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.

1. Say that 26 cannot be divided by 10.
2. Give the answer as a decimal fraction or a mixed numberIn algebra, a vulgar fraction consists of one integer divided by a non-zero integer. The fraction "three divided by four" or "three over four" or "three fourths" or "three quarters" can be written as : :or 3 ÷ 4 :or 3/4 :or 3 In this article, we will use, so 26 ÷ 10 = 2.6 or . This is the approach usually taken in mathematics.
3. 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 moduloModular arithmetic Group theory In mathematics, modular arithmetic is a system of arithmetic for certain equivalence classes of integers, called congruence classes . In modular arithmetic, numbers 'wrap around' after they reach a certain value (the modulu 10 (or 26i % 10i) is given as 6.