Ignoring the order of the two fractions, the only pairings are \(\displaystyle (\frac12,\frac34)\), \(\displaystyle (\frac13,\frac24)\) and \(\displaystyle (\frac14,\frac23)\). Each pairing uses every digit once.

Their positive differences are \(\displaystyle \frac14\), \(\displaystyle \frac16\) and \(\displaystyle \frac5{12}\), respectively.

Using twelfths gives gaps \(\displaystyle \frac3{12},\frac2{12},\frac5{12}\). The middle pairing has the smallest difference.

Answer

The pair is \(\displaystyle \frac13\) and \(\displaystyle \frac24\), with difference \(\displaystyle \frac16\).