\[\boxed{\mathbf{2.2}\mathbf{50}}\]
\[\textbf{а)}\ 38\frac{1^{\backslash 3}}{8} + 4\frac{5}{24} =\]
\[= 38\frac{3}{24} + 4\frac{5}{24} = 42\frac{8}{24} = 42\frac{1}{3}\]
\[\textbf{б)}\ 4\frac{19^{\backslash 3}}{75} + 6\frac{17^{\backslash 5}}{45} =\]
\[= 4\frac{57}{225} + 6\frac{85}{225} = 10\frac{142}{225}\]
\[\textbf{в)}\ 47\frac{3^{\backslash 3}}{14} + 1\frac{8^{\backslash 2}}{21} =\]
\[= 47\frac{9}{42} + 1\frac{16}{42} = 48\frac{25}{42}\]
\[\textbf{г)}\ 54\frac{3^{\backslash 3}}{4} + 18\frac{5^{\backslash 2}}{6} =\]
\[= 54\frac{9}{12} + 18\frac{10}{12} = 72\frac{19}{12} =\]
\[= 73\frac{7}{12}\]
\[\textbf{д)}\ 28\frac{5^{\backslash 4}}{9} + 13\frac{3^{\backslash 9}}{4} =\]
\[= 28\frac{20}{36} + 13\frac{27}{36} = 41\frac{47}{36} =\]
\[= 42\frac{11}{36}\]
\[\textbf{е)}\ \frac{4^{\backslash 5}}{7} + 2\frac{3^{\backslash 7}}{5} = \frac{20}{35} + 2\frac{21}{35} =\]
\[= 2\frac{41}{35} = 3\frac{6}{35}\]
\[\textbf{ж)}\ 9 + 2\frac{2}{9} = 11\frac{2}{9}\]
\[\textbf{з)}\ 3\frac{11}{24} + \frac{1^{\backslash 4}}{6} = 3\frac{11}{24} + \frac{4}{24} =\]
\[= 3\frac{15}{24} = 3\frac{5}{8}\]