\[\boxed{\mathbf{1.\ }}\]
\[1)\ \frac{5 \cdot 2}{15} = \frac{2}{3}\]
\[2)\ \frac{6 \cdot 7}{7 \cdot 8} = \frac{3}{4}\]
\[3)\ \frac{4 \cdot 9}{27 \cdot 2} = \frac{2}{3}\]
\[4)\ \frac{10 \cdot 18}{36 \cdot 25} = \frac{2}{10} = \frac{1}{5}\]
\[\boxed{\mathbf{2.\ }}\]
\[1)\ 1\frac{1}{2} = \frac{3}{2}\]
\[2)\ 4\frac{3}{4} = \frac{19}{4}\]
\[3)\ 7\frac{5}{6} = \frac{47}{6}\]
\[4)\ 2\frac{1}{17} = \frac{35}{17}\]
\[\boxed{\mathbf{3.\ }}\]
\[1)\ \frac{35}{8} = 4\frac{3}{8}\]
\[2)\ \frac{13}{9} = 1\frac{4}{9}\]
\[3)\ \frac{23}{6} = 3\frac{5}{6}\]
\[4)\ \frac{69}{13} = 5\frac{4}{13}\]
\[\boxed{\mathbf{4.\ }}\]
\[\frac{1}{6} < \frac{x}{12} < \frac{1}{2}\]
\[\frac{2}{12} < \frac{x}{12} < \frac{6}{12}\]
\[\frac{3}{12};\frac{4}{12};\frac{5}{12}.\]