$\frac{8}{9} * \frac{3}{5} = \frac{8 * \overset{1}{\bcancel{3}}}{\underset{3}{\bcancel{9}} * 5} = \frac{8 * 1}{3 * 5} = \frac{8}{15}$

$\frac{9}{2} * \frac{2}{9} = \frac{\overset{1}{\bcancel{9}} * \overset{1}{\bcancel{2}}}{\underset{1}{\bcancel{2}} * \underset{1}{\bcancel{9}}} = \frac{1}{1} = 1$

$\frac{8}{21} * \frac{7}{10} = \frac{\overset{4}{\bcancel{8}} * \overset{1}{\bcancel{7}}}{\underset{3}{\bcancel{21}} * \underset{5}{\bcancel{10}}} = \frac{4 * 1}{3 * 5} = \frac{4}{15}$

$\frac{8}{15} * \frac{25}{28} = \frac{\overset{2}{\bcancel{8}} * \overset{5}{\bcancel{25}}}{\underset{3}{\bcancel{15}} * \underset{7}{\bcancel{28}}} = \frac{2 * 5}{3 * 7} = \frac{10}{21}$

$\frac{2}{15} * \frac{5}{22} = \frac{\overset{1}{\bcancel{2}} * \overset{1}{\bcancel{5}}}{\underset{3}{\bcancel{15}} * \underset{11}{\bcancel{22}}} = \frac{1 * 1}{3 * 11} = \frac{1}{33}$