\[\boxed{\mathbf{1.}}\]
\[\boxed{\mathbf{2.}}\]
\[\frac{2}{7} < \frac{6}{7}\]
\[\frac{5}{6} > \frac{5}{8}\]
\[\frac{9}{11} < \frac{11}{9}\]
\[1\frac{3}{4} < 3\frac{1}{4}\]
\[m - \frac{1}{3} > m - \frac{2}{3}\]
\[\frac{4}{5} - c > \frac{4}{9} - c\]
\[\boxed{\mathbf{3.}}\]
\[\textbf{а)}\ \frac{11}{4} = 2\frac{3}{4}\]
\[\frac{105}{29} = 3\frac{18}{29}\]
\[\textbf{б)}\ 1\frac{2}{3} = \frac{5}{3}\]
\[4\frac{5}{12} = \frac{53}{12}\]
\[\boxed{\mathbf{4.}}\]
\[2\frac{6}{11} + (7 - a) = 4\frac{2}{11}\]
\[7 - a = 4\frac{2}{11} - 2\frac{6}{11}\]
\[7 - a = 3\frac{13}{11} - 2\frac{6}{11}\]
\[7 - a = 1\frac{7}{11}\]
\[a = 6\frac{11}{11} - 1\frac{7}{11}\]
\[a = 5\frac{4}{11}.\]
\[\boxed{\mathbf{5.}}\]
\[1)\ 4\frac{2}{5} + 1\frac{3}{5} = 5\frac{5}{5} = 6\ (см) -\]
\[вторая\ сторона\ треугольника.\]
\[2)\ 14\frac{1}{5} - \left( 4\frac{2}{5} + 6 \right) =\]
\[= 13\frac{6}{5} - 10\frac{2}{5} = 3\frac{4}{5}\ (см) -\]
\[третья\ сторона.\]
\[Ответ:3\frac{4}{5}\ см.\]
\[\boxed{\mathbf{6.}}\]
\[\frac{1}{3} = \frac{4}{12}\]