a.

$\frac{7}{8} - \frac{1}{3} = \frac{14}{16} - \frac{6}{16} = \frac{8}{16}$;    

$\frac{8}{9} + \frac{2}{5}= \frac{32}{45} + \frac{18}{45} = \frac{50}{45}$

$\frac{3}{10}\times \frac{1}{6} = \frac{3\times 1}{10\times 6} = \frac{3}{60}$;  

$\frac{8}{9} : \frac{3}{7} = \frac{8}{9}\times \frac{7}{3} = \frac{56}{27}$

b.

$1\frac{2}{7} + 6\frac{5}{6}=\frac{9}{7}+\frac{41}{6}=\frac{54}{42}+\frac{287}{42}=\frac{329}{42}$

$5\frac{3}{4} - \frac{1}{5}=\frac{23}{4}- \frac{1}{5}=\frac{115}{20}-\frac{4}{20}=\frac{111}{20}$

$6\frac{2}{9} : 4\frac{7}{10}=\frac{56}{9}:\frac{47}{10}=\frac{56}{9}\times \frac{10}{47}=\frac{560}{523}$

$\frac{5}{3} + \frac{3}{2} - \frac{7}{6} = \frac{10}{6} + \frac{9}{6} - \frac{7}{6}  = \frac{12}{6}$;