a)

$\frac{6}{13}+\frac{7}{13}=\frac{13}{13}=1$

$\frac{5}{9}+\frac{2}{3}=\frac{5}{9}+\frac{6}{9}=\frac{11}{9}=1\frac{2}{9}$

$6\frac{3}{4}+\frac{5}{12}=6\frac{9}{12}+\frac{5}{12}=6\frac{14}{12}=7\frac{2}{12}-7\frac{1}{6}$

$3\frac{5}{8}+2\frac{1}{4}=3\frac{5}{8}+2\frac{2}{8}=5\frac{7}{8}$

b)

$\frac{1}{5}-\frac{1}{10}=\frac{2}{10}-\frac{1}{10}=\frac{1}{10}$

$\frac{7}{8}-\frac{15}{32}=\frac{28}{32}-\frac{15}{32}=\frac{13}{32}$