You can also get the reciprocal of a fraction by flipping the fraction, or equivalently, the reciprocal of a number can be defined as that number taken to the power of -1.
The reciprocal of <sup>2</sup>⁄<sub>3</sub> is <sup>3</sup>⁄<sub>2</sub> since 1/(<sup>2</sup>⁄<sub>3</sub>) = <sup>3</sup>/<sub>2</sub>, or (<sup>2</sup>⁄<sub>3</sub>)<sup>-1</sup> = <sup>3</sup>/<sub>2</sub>.
The reciprocal of 23 is <sup>1</sup>⁄<sub>23</sub>. Now if we look at the reciprocal of <sup>1</sup>⁄<sub>23</sub> we get <sup>23</sup>⁄<sub>1</sub>, which is the original number.