Division (arithmetic)

In arithmetic, division is the operation of finding how many copies of one quantity or number are needed to make up another. This may be viewed as a process of repeated subtraction: the divisor is repeatedly subtracted from the dividend until this can be done no longer; the number of times the subtraction was performed is the quotient and whatever is left over is the . If the remainder is zero, then the division is said to be exact. In any event, the remainder will be less than the divisor.

For example, 13 (dividend) may be divided 4 (divisor) by repeatedly subtracting 4: 13-4 = 9, 9-4 = 5, 5-4 = 1, at which point the process must terminate, with a quotient of 3 and remainder of 1.

Division may also be viewed as the inverse operation to multiplication, seen as repeated addition. Symbolically, if c is the product of a and b,


 * $$a \times b = c ,\,$$

then a is the answer to the questions "How many times must b be added to make c" or "How many copies of b make up c" or "By what must b be multiplied to yield c". We write


 * $$c / b = a \,$$

or
 * $$c \div b = a .\,$$

See also Divisor.