The multiplication of two numbers,  a  and  b , is denoted as

where  c  the result of multiplication is also known as the product of  a  and  b  (or the sum of  a  and  b); the quantities  a  and  b  are called factors or multipliers.

If  n  is an integer then the product  n·a  means the sum of  n  equal quantities  a:

.

The product of  n  equal multipliers  a  is denoted as  an:

.

The division of  a  by  b  is denoted by any of the following formulas,

.

In the above formulas,  c  is the result of division (or quotient);  a  is called the dividend;  b  is the divisor.

Two quantities are called the reciprocal of each other if their product equals unity. So the quotient 1/a  is the reciprocal of  a and vice versa.

The operation of division can be expressed in terms of multiplication,

.

That is, to divide  a  by  b  means to multiply  a  by the reciprocal of  b.

The result of division can be easily controlled:

c = a / b    if and only if    c b = a.

If two operations, the multiplication by a number and division by the number, follow one after another, then they cancel each other:

.

Therefore, the multiplication and division are the inverse operations with respect to each other (or the mutually inverse operations).

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