\[\boxed{\mathbf{2.}\mathbf{57}}\]
\[\textbf{а)}\ \frac{4}{9} + \frac{7}{9} - \frac{1}{9} = \frac{4 + 7 - 1}{9} =\]
\[= \frac{10}{9} = 1\frac{1}{9}\]
\[\textbf{б)}\ \frac{6}{7} - \left( \frac{5}{7} - \frac{1}{7} \right) = \frac{6}{7} - \frac{5}{7} + \frac{1}{7} =\]
\[= \frac{6 - 5 + 1}{7} = \frac{2}{7}\]
\[\textbf{в)}\ 5\frac{6}{39} + 4\frac{7}{39} = 9\frac{6 + 7}{39} =\]
\[= 9\frac{13}{39} = 9\frac{1}{3}\]
\[\textbf{г)}\ 7\frac{13}{15} - 3\frac{8}{15} = 4\frac{13 - 8}{15} =\]
\[= 4\frac{5}{15} = 4\frac{1}{3}\]