<P> In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1 / x or x, is a number which when multiplied by x yields the multiplicative identity, 1 . The multiplicative inverse of a fraction a / b is b / a . For the multiplicative inverse of a real number, divide 1 by the number . For example, the reciprocal of 5 is one fifth (1 / 5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4 . The reciprocal function, the function f (x) that maps x to 1 / x, is one of the simplest examples of a function which is its own inverse (an involution). </P> <P> The term reciprocal was in common use at least as far back as the third edition of Encyclopædia Britannica (1797) to describe two numbers whose product is 1; geometrical quantities in inverse proportion are described as reciprocall in a 1570 translation of Euclid's Elements . </P>

The product of a rational number and its multiplicative inverse is