A reciprocal is the inverse of a number: it is the number turned upside down.

A reciprocal of an integer turns the number into a fraction, where the numerator is 1 and the denominator is the original number:

• the reciprocal of 12 is `frac(1)(12)`

For a fraction, the numerator and denominator change places:

• the reciprocal of `frac(3)(4)` is `frac(4)(3)`

Multiplying a number and its reciprocal always gives an answer of 1:

`12 xx frac(1)(12)=frac(12)(12) = 1`

`frac(3)(4) xxfrac(4)(3)=frac(12)(12) = 1`

Zero does not have a reciprocal.

The reciprocal is also known as the Multiplicative Inverse. A number multiplied by its inverse gives the Multiplicative Identity, which is 1.