4. Выполните действия: а) $$7-4\frac{4}{5}$$; б) $$4\frac{3}{10}+1\frac{1}{12}$$; в) $$3\frac{5}{7} \cdot 1\frac{1}{13}$$; г) $$16\frac{1}{3}:5\frac{5}{6}$$

а) $$7-4\frac{4}{5} = 7 - \frac{4 \cdot 5 + 4}{5} = 7 - \frac{24}{5} = \frac{7 \cdot 5}{5} - \frac{24}{5} = \frac{35}{5} - \frac{24}{5} = \frac{35-24}{5} = \frac{11}{5} = 2\frac{1}{5}$$

б) $$4\frac{3}{10}+1\frac{1}{12} = \frac{4 \cdot 10 + 3}{10} + \frac{1 \cdot 12 + 1}{12} = \frac{43}{10} + \frac{13}{12} = \frac{43 \cdot 6}{10 \cdot 6} + \frac{13 \cdot 5}{12 \cdot 5} = \frac{258}{60} + \frac{65}{60} = \frac{258+65}{60} = \frac{323}{60} = 5\frac{23}{60}$$

в) $$3\frac{5}{7} \cdot 1\frac{1}{13} = \frac{3 \cdot 7 + 5}{7} \cdot \frac{1 \cdot 13 + 1}{13} = \frac{26}{7} \cdot \frac{14}{13} = \frac{26 \cdot 14}{7 \cdot 13} = \frac{2 \cdot 13 \cdot 2 \cdot 7}{7 \cdot 13} = 2 \cdot 2 = 4$$

г) $$16\frac{1}{3}:5\frac{5}{6} = \frac{16 \cdot 3 + 1}{3} : \frac{5 \cdot 6 + 5}{6} = \frac{49}{3} : \frac{35}{6} = \frac{49}{3} \cdot \frac{6}{35} = \frac{49 \cdot 6}{3 \cdot 35} = \frac{7 \cdot 7 \cdot 2 \cdot 3}{3 \cdot 5 \cdot 7} = \frac{7 \cdot 2}{5} = \frac{14}{5} = 2\frac{4}{5}$$