80. Найдите значение выражения: 1) 2\frac{2}{3} \cdot \frac{2}{9} : \frac{1}{4}; 2) 2\frac{2}{9} : (\frac{2}{1}:\frac{4}{1}); 3) (7\frac{5}{7}:8\frac{3}{7}-\frac{1}{7}):1\frac{1}{3}; 4) (4\frac{5}{12}-3\frac{13}{24}):1\frac{3}{6}+\frac{5}{7} \cdot \frac{5}{7}.

80. Найдите значение выражения:

1) $$2\frac{2}{3} \cdot \frac{2}{9} : \frac{1}{4}=\frac{2 \cdot 3+2}{3} \cdot \frac{2}{9} : \frac{1}{4}=\frac{8}{3} \cdot \frac{2}{9} \cdot \frac{4}{1}=\frac{8}{3} \cdot \frac{2}{9} \cdot \frac{4}{1}=\frac{64}{27}=2\frac{10}{27}$$

Ответ: $$2\frac{10}{27}$$

2) $$2\frac{2}{9} : (\frac{2}{1}:\frac{4}{1})=\frac{2 \cdot 9+2}{9} : (\frac{2}{1} \cdot \frac{1}{4})=\frac{20}{9}:(\frac{2}{1} \cdot \frac{1}{4})=\frac{20}{9}:\frac{2}{4}=\frac{20}{9} \cdot \frac{4}{2}=\frac{20}{9} \cdot \frac{2}{1}=\frac{40}{9}=4\frac{4}{9}$$

Ответ: $$4\frac{4}{9}$$

3) $$(7\frac{5}{7}:8\frac{3}{7}-\frac{1}{7}):1\frac{1}{3}=(\frac{7 \cdot 7+5}{7}:\frac{8 \cdot 7+3}{7}-\frac{1}{7}):\frac{1 \cdot 3+1}{3}=(\frac{49+5}{7}:\frac{56+3}{7}-\frac{1}{7}):\frac{4}{3}=(\frac{54}{7}:\frac{59}{7}-\frac{1}{7}):\frac{4}{3}=(\frac{54}{7} \cdot \frac{7}{59}-\frac{1}{7}):\frac{4}{3}=(\frac{54}{59}-\frac{1}{7}):\frac{4}{3}=(\frac{54 \cdot 7}{59 \cdot 7}-\frac{1 \cdot 59}{7 \cdot 59}):\frac{4}{3}=(\frac{378}{413}-\frac{59}{413}):\frac{4}{3}=\frac{319}{413}:\frac{4}{3}=\frac{319}{413} \cdot \frac{3}{4}=\frac{957}{1652}$$

Ответ: $$\frac{957}{1652}$$

4) $$(4\frac{5}{12}-3\frac{13}{24}):1\frac{3}{6}+\frac{5}{7} \cdot \frac{5}{7}=(\frac{4 \cdot 12+5}{12}-\frac{3 \cdot 24+13}{24}):\frac{1 \cdot 6+3}{6}+\frac{25}{49}=(\frac{48+5}{12}-\frac{72+13}{24}):\frac{9}{6}+\frac{25}{49}=(\frac{53}{12}-\frac{85}{24}):\frac{9}{6}+\frac{25}{49}=(\frac{53 \cdot 2}{12 \cdot 2}-\frac{85}{24}):\frac{9}{6}+\frac{25}{49}=(\frac{106}{24}-\frac{85}{24}):\frac{9}{6}+\frac{25}{49}=\frac{21}{24}:\frac{9}{6}+\frac{25}{49}=\frac{21}{24} \cdot \frac{6}{9}+\frac{25}{49}=\frac{7 \cdot 3}{4 \cdot 6} \cdot \frac{6}{3 \cdot 3}+\frac{25}{49}=\frac{7}{4} \cdot \frac{1}{3}+\frac{25}{49}=\frac{7}{12}+\frac{25}{49}=\frac{7 \cdot 49}{12 \cdot 49}+\frac{25 \cdot 12}{49 \cdot 12}=\frac{343}{588}+\frac{300}{588}=\frac{643}{588}=1\frac{55}{588}$$

Ответ: $$1\frac{55}{588}$$