a) $\frac{5}{9}:\frac{7}{3} = \frac{5}{9} \times \frac{3}{7} = \frac{{15}}{{63}} = \frac{5}{{21}}$
b) $\frac{2}{7}:\frac{8}{5} = \frac{2}{7} \times \frac{5}{8} = \frac{{10}}{{56}} = \frac{5}{{28}}$
c) $\frac{4}{{15}}:\frac{2}{5} = \frac{4}{{15}} \times \frac{5}{2} = \frac{{20}}{{30}} = \frac{2}{3}$
d) $\frac{7}{9}:\frac{{21}}{9} = \frac{7}{9} \times \frac{9}{{21}} = \frac{{63}}{{189}} = \frac{1}{3}$