Решим примеры по действиям:
а) $$\frac{4}{5} \div 1\frac{1}{3} + 2\frac{1}{3} \cdot \frac{3}{7} - 1 \div 1\frac{3}{8}$$;
1) $$\frac{4}{5} \div 1\frac{1}{3} = \frac{4}{5} \div \frac{4}{3} = \frac{4}{5} \cdot \frac{3}{4} = \frac{4 \cdot 3}{5 \cdot 4} = \frac{3}{5}$$;
2) $$2\frac{1}{3} \cdot \frac{3}{7} = \frac{7}{3} \cdot \frac{3}{7} = \frac{7 \cdot 3}{3 \cdot 7} = 1$$;
3) $$1 \div 1\frac{3}{8} = 1 \div \frac{11}{8} = 1 \cdot \frac{8}{11} = \frac{8}{11}$$;
4) $$\frac{3}{5} + 1 - \frac{8}{11} = \frac{3}{5} + \frac{5}{5} - \frac{8}{11} = \frac{8}{5} - \frac{8}{11} = \frac{88}{55} - \frac{40}{55} = \frac{48}{55}$$.
Ответ: $$\frac{48}{55}$$.
б) $$2\frac{1}{6} \div (1\frac{1}{15} - \frac{1}{5}) + (2\frac{1}{8} + \frac{3}{4}) \div 5\frac{3}{4}$$;
1) $$1\frac{1}{15} - \frac{1}{5} = \frac{16}{15} - \frac{3}{15} = \frac{13}{15}$$;
2) $$2\frac{1}{6} \div \frac{13}{15} = \frac{13}{6} \div \frac{13}{15} = \frac{13}{6} \cdot \frac{15}{13} = \frac{13 \cdot 15}{6 \cdot 13} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}$$;
3) $$2\frac{1}{8} + \frac{3}{4} = \frac{17}{8} + \frac{6}{8} = \frac{23}{8}$$;
4) $$5\frac{3}{4} = \frac{23}{4}$$;
5) $$\frac{23}{8} \div \frac{23}{4} = \frac{23}{8} \cdot \frac{4}{23} = \frac{23 \cdot 4}{8 \cdot 23} = \frac{4}{8} = \frac{1}{2}$$;
6) $$2\frac{1}{2} + \frac{1}{2} = \frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3$$.
Ответ: 3.