777. Решите уравнение: a) $$2\frac{1}{3}k=4\frac{1}{2}\cdot1\frac{1}{9}$$; B) $$y:\frac{4}{5}=3\frac{3}{8}:1\frac{1}{4}$$; б) $$8\frac{1}{2}m = 3\frac{2}{3}\cdot1\frac{1}{11}$$; г) $$z:\frac{3}{14}=3\frac{4}{9}:\frac{4}{9}$$.

1. Решение уравнения a):
   • $$2\frac{1}{3}k=4\frac{1}{2}\cdot1\frac{1}{9}$$
   • $$\frac{7}{3}k = \frac{9}{2} \cdot \frac{10}{9}$$
   • $$\frac{7}{3}k = \frac{90}{18} = 5$$
   • $$k = 5 : \frac{7}{3} = 5 \cdot \frac{3}{7}$$
   • $$k = \frac{15}{7} = 2\frac{1}{7}$$
2. Решение уравнения б):
   • $$8\frac{1}{2}m = 3\frac{2}{3}\cdot1\frac{1}{11}$$
   • $$\frac{17}{2}m = \frac{11}{3} \cdot \frac{12}{11}$$
   • $$\frac{17}{2}m = \frac{132}{33} = 4$$
   • $$m = 4 : \frac{17}{2} = 4 \cdot \frac{2}{17}$$
   • $$m = \frac{8}{17}$$
3. Решение уравнения в):
   • $$y:\frac{4}{5}=3\frac{3}{8}:1\frac{1}{4}$$
   • $$y:\frac{4}{5}=\frac{27}{8}:\frac{5}{4}$$
   • $$y:\frac{4}{5}=\frac{27}{8} \cdot \frac{4}{5}$$
   • $$y:\frac{4}{5}=\frac{108}{40} = \frac{27}{10}$$
   • $$y = \frac{27}{10} \cdot \frac{4}{5}$$
   • $$y = \frac{108}{50} = \frac{54}{25} = 2\frac{4}{25}$$
4. Решение уравнения г):
   • $$z:\frac{3}{14}=3\frac{4}{9}:\frac{4}{9}$$
   • $$z:\frac{3}{14}=\frac{31}{9}:\frac{4}{9}$$
   • $$z:\frac{3}{14}=\frac{31}{9} \cdot \frac{9}{4}$$
   • $$z:\frac{3}{14}=\frac{279}{36} = \frac{31}{4}$$
   • $$z = \frac{31}{4} \cdot \frac{3}{14}$$
   • $$z = \frac{93}{56} = 1\frac{37}{56}$$

Ответ: a) $$k = 2\frac{1}{7}$$; б) $$m = \frac{8}{17}$$; в) $$y = 2\frac{4}{25}$$; г) $$z = 1\frac{37}{56}$$.