Division (arithmetic)

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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 remainder. 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',

<math>a \times b = c ,\,</math>

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

<math>c / b = a \,</math>

or

<math>c \div b = a .\,</math>