Fraccionando problemas

a) $$\frac{1}{2}+ \frac{2}{3} = \frac{3·1+2·2}{2·3}=\frac{3+4}{6}=\boxed{\frac{7}{6}}$$

b) $$\left({\displaystyle \frac{1}{5}}·{\displaystyle \frac{2}{3}}\right) + \frac{1}{15} = \frac{2}{15} + \frac{1}{15} = \frac{3}{15} = \boxed{\frac{1}{5}}$$

c) $$\frac{{\displaystyle \frac{1}{5}}}{{\displaystyle \frac{2}{7}}}·\frac{1}{2}=\frac{1·7}{5·2}·\frac{1}{2}=\frac{7}{10}·\frac{1}{2}=\boxed{\frac{7}{20}}$$

d) $$\frac{\left(4+{\displaystyle \frac{2}{3}}\right)}{\left({\displaystyle \frac{7}{2}}-{\displaystyle \frac{1}{3}}\right)} =\frac{{\displaystyle \frac{12+2}{3}}}{{\displaystyle \frac{21-2}{6}}} = \frac{{\displaystyle \frac{14}{3}}}{{\displaystyle \frac{19}{6}}} =\frac{14 · 6}{19 ·3} =\frac{84}{57}= \boxed{\frac{28}{19}}$$