The smallest fraction, which should be added to the sum of $$2\frac{1}{2},\,3\frac{1}{3},\,4\frac{1}{4}$$   and $$5\frac{1}{5}$$ to make the result a whole number, is.

$$\eqalign{ & 2\frac{1}{2} + 3\frac{1}{3} + 4\frac{1}{4} + 5\frac{1}{5} \cr & = \left( {2 + 3 + 4 + 5} \right) + \left( {\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}} \right) \cr & = 14 + \left( {\frac{{30 + 20 + 15 + 12}}{{60}}} \right) \cr & = 14 + \frac{{77}}{{60}} \cr & = 14 + 1 + \frac{{17}}{{60}} \cr & = 15 + \frac{{17}}{{60}} \cr & \therefore {\text{Required answer}} = 1 - \frac{{17}}{{60}} \cr & = \frac{{60 - 17}}{{60}} \cr & = \frac{{43}}{{60}} \cr} $$