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$\big(3,\overline6 : \frac{33}{2}+0,\overline6\big)\big(0,5·\frac{2}{7}+\frac{0,05}{7}\big)$ =
=$ \big(\frac{36-3}{9} : \frac{33}{2}+\frac{6-0}{9}\big)\big(\frac{5}{10}·\frac{2}{7}+\frac{5}{700}\big)$ =
=$ \big(\frac{33}{9} · \frac{2}{33}+\frac{6}{9}\big)\big(\frac{1}{2}·\frac{2}{7}+\frac{1}{140}\big)$ =
=$ \big(\frac{11}{3} · \frac{2}{33}+\frac{2}{3}\big)\big(\frac{1}{1}·\frac{1}{7}+\frac{1}{140}\big)$ =
=$ \big(\frac{1}{3} · \frac{2}{3}+\frac{2}{3}\big)\big(\frac{1}{7}+\frac{1}{140}\big)$ =
=$ \big(\frac{2}{9}+\frac{2}{3}\big)\big(\frac{20+1}{140}\big)$ =
=$ \big(\frac{2+6}{9}\big)·\frac{21}{140}$ =
=$ \frac{8}{9}·\frac{3}{20}$ =
=$ \frac{2}{3}·\frac{1}{5}$ =
=$ \frac{2}{15}$