$(\frac{3}{4} + \frac{1}{6}) * 3 + (\frac{5}{6} - \frac{1}{2}) : \frac{2}{9} = (\frac{9}{12} + \frac{2}{12}) * 3 + (\frac{5}{6} - \frac{3}{6}) * \frac{9}{2} = \frac{11}{12} * 3 + \frac{2}{6} * \frac{9}{2} = \frac{11}{4} + \frac{1}{2} * \frac{3}{1} = 2\frac{3}{4} + \frac{3}{2} = 2\frac{3}{4} + 1\frac{1}{2} = 2\frac{3}{4} + 1\frac{2}{4} = 3\frac{5}{4} = 4\frac{1}{4}$

$(1\frac{1}{5} + 2\frac{3}{10}) : \frac{1}{2} + (6\frac{3}{4} - 2\frac{2}{3}) : 1\frac{1}{6} = (1\frac{2}{10} + 2\frac{3}{10}) * \frac{2}{1} + (6\frac{9}{12} - 2\frac{8}{12}) : \frac{7}{6} = 3\frac{5}{10} * \frac{2}{1} + 4\frac{1}{12} * \frac{6}{7} = 3\frac{1}{2} * \frac{2}{1} + \frac{49}{12} * \frac{6}{7} = \frac{7}{2} * \frac{2}{1} + \frac{7}{2} * \frac{1}{1} = \frac{7}{1} * \frac{1}{1} + 3\frac{1}{2} = 10\frac{1}{2}$