(3\frac{1}{4}+4\frac{2}{3}):2\frac{1}{6}= (1\frac{3}{4}-\frac{2}{9})\cdot 1\frac{4}{5}= (4\frac{7}{8}+5\frac{3}{5}):4\frac{3}{40}= (5\frac{6}{11}-4\frac{3}{22})\cdot \frac{33}{35}= (3\frac{9}{14}-2\frac{4}{5}):7\frac{1}{3}= (2\frac{13}{15}+6\frac{5}{6}):5\frac{3}{5}=

Выполним действия:

1. $$(3\frac{1}{4}+4\frac{2}{3}):2\frac{1}{6}=(3\frac{3}{12}+4\frac{8}{12}):2\frac{1}{6}=7\frac{11}{12}:2\frac{1}{6}=\frac{95}{12}:\frac{13}{6}=\frac{95}{12}\cdot \frac{6}{13}=\frac{95}{2}\cdot \frac{1}{13}=\frac{95}{26}=3\frac{17}{26}$$
2. $$(1\frac{3}{4}-\frac{2}{9})\cdot 1\frac{4}{5}=(\frac{7}{4}-\frac{2}{9})\cdot \frac{9}{5}=(\frac{63}{36}-\frac{8}{36})\cdot \frac{9}{5}=\frac{55}{36}\cdot \frac{9}{5}=\frac{11}{4}\cdot \frac{1}{1}=\frac{11}{4}=2\frac{3}{4}$$
3. $$(4\frac{7}{8}+5\frac{3}{5}):4\frac{3}{40}=(4\frac{35}{40}+5\frac{24}{40}):4\frac{3}{40}=9\frac{59}{40}:4\frac{3}{40}=10\frac{19}{40}:4\frac{3}{40}=\frac{419}{40}:\frac{163}{40}=\frac{419}{40}\cdot \frac{40}{163}=\frac{419}{163}=2\frac{93}{163}$$
4. $$(5\frac{6}{11}-4\frac{3}{22})\cdot \frac{33}{35}=(5\frac{12}{22}-4\frac{3}{22})\cdot \frac{33}{35}=1\frac{9}{22}\cdot \frac{33}{35}=\frac{31}{22}\cdot \frac{33}{35}=\frac{31}{2}\cdot \frac{3}{35}=\frac{93}{70}=1\frac{23}{70}$$
5. $$(3\frac{9}{14}-2\frac{4}{5}):7\frac{1}{3}=(3\frac{45}{70}-2\frac{56}{70}):7\frac{1}{3}=(2\frac{115}{70}-2\frac{56}{70}):7\frac{1}{3}=\frac{59}{70}:7\frac{1}{3}=\frac{59}{70}:\frac{22}{3}=\frac{59}{70}\cdot \frac{3}{22}=\frac{177}{1540}$$
6. $$(2\frac{13}{15}+6\frac{5}{6}):5\frac{3}{5}=(2\frac{26}{30}+6\frac{25}{30}):5\frac{3}{5}=8\frac{51}{30}:5\frac{3}{5}=9\frac{21}{30}:5\frac{3}{5}=9\frac{7}{10}:5\frac{3}{5}=\frac{97}{10}:\frac{28}{5}=\frac{97}{10}\cdot \frac{5}{28}=\frac{97}{2}\cdot \frac{1}{28}=\frac{97}{56}=1\frac{41}{56}$$

Ответ: $$3\frac{17}{26}$$, $$2\frac{3}{4}$$, $$2\frac{93}{163}$$, $$1\frac{23}{70}$$, $$\frac{177}{1540}$$, $$1\frac{41}{56}$$