\[\boxed{\mathbf{872\ (872)}\mathbf{.}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[\textbf{а)}\ 999 \cdot \frac{3}{4}\ \ \ и\ \ 999\ :\frac{3}{4}\]
\[999\ :\frac{3}{4} = 999 \cdot \frac{4}{3}\]
\[Тогда\ 999 \cdot \frac{3}{4} < 999\ :\frac{3}{4}.\]
\[\textbf{б)}\frac{5}{7} \cdot 1\frac{1}{8}\ \ \ и\ \ \ \ \frac{5}{7}\ :1\frac{1}{8}\]
\[1\frac{1}{8} = \frac{9}{8};\ \ \ \ тогда\ \ \ \ \ \ \frac{5}{7} \cdot \frac{9}{8}\ \ \ \ \ и\ \ \ \ \ \ \frac{5}{7}\ :\frac{9}{8}\]
\[\frac{5}{7}\ :\frac{9}{8} = \frac{5}{7} \cdot \ \frac{8}{9}\]
\[Тогда\frac{5}{7} \cdot 1\frac{1}{8} > \frac{5}{7}\ :1\frac{1}{8}.\]
\[\textbf{в)}\frac{20}{9}\ \ \ и\ \ \ \ \left( \frac{20}{9} \right)^{2}\]
\[\left( \frac{20}{9} \right)^{2} = \frac{400}{81}\]
\[Тогда\ \ \ \frac{20}{9} < \left( \frac{20}{9} \right)^{2}.\]
\[\textbf{г)}\ 15\ :\frac{7}{8}\ \ \ \ и\ \ \ \ 15\ :\left( \frac{7}{8} \right)^{2}\]
\[\left( \frac{7}{8} \right)^{2} = \frac{49}{64};\ \ \ \ \ \ 15\ :\frac{49}{64}\]
\[Тогда\ 15\ :\frac{7}{8} < 15\ \ :\left( \frac{7}{8} \right)^{2}.\]