$\frac{1}{3} + \frac{1}{8} = \frac{1 * 8 + 1 * 3}{24} = \frac{11}{24}$;
$\frac{1}{4} + \frac{1}{7} = \frac{1 * 7 + 1 * 4}{28} = \frac{11}{28}$;
$\frac{1}{5} + \frac{1}{6} = \frac{1 * 6 + 1 * 5}{30} = \frac{11}{30}$;
$\frac{1}{2} + \frac{1}{9} = \frac{1 * 9 + 1 * 2}{18} = \frac{11}{18}$.
$\frac{11}{30} < \frac{11}{28} < \frac{11}{24} < \frac{11}{18}$, значит:
$\frac{1}{5} + \frac{1}{6} < \frac{1}{4} + \frac{1}{7} < \frac{1}{3} + \frac{1}{8} < \frac{1}{2} + \frac{1}{9}$