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.
What is the reciprocal of 10?
Turn the number into a fraction: `frac(10)(1)`.
Then swap the numerator and the denominator for the reciprocal `frac(1)(10)`
What is the reciprocal of -`frac(1)(4)`?
Note that the answer remains negative. Reverse the numerator and denominator for the receiprocal.
See also Inverse Functions