Решение

1. $$\frac{4}{15} + \frac{3}{4} = \frac{4 \cdot 4 + 3 \cdot 15}{15 \cdot 4} = \frac{16 + 45}{60} = \frac{61}{60} = 1\frac{1}{60}$$
2. $$\frac{5}{6} - \frac{9}{14} = \frac{5 \cdot 7 - 9 \cdot 3}{6 \cdot 7} = \frac{35 - 27}{42} = \frac{8}{42} = \frac{4}{21}$$
3. $$4\frac{4}{7} + 6\frac{1}{4} = \frac{4 \cdot 7 + 4}{7} + \frac{6 \cdot 4 + 1}{4} = \frac{28 + 4}{7} + \frac{24 + 1}{4} = \frac{32}{7} + \frac{25}{4} = \frac{32 \cdot 4 + 25 \cdot 7}{7 \cdot 4} = \frac{128 + 175}{28} = \frac{303}{28} = 10\frac{23}{28}$$
4. $$5\frac{7}{8} - 3\frac{5}{6} = \frac{5 \cdot 8 + 7}{8} - \frac{3 \cdot 6 + 5}{6} = \frac{40 + 7}{8} - \frac{18 + 5}{6} = \frac{47}{8} - \frac{23}{6} = \frac{47 \cdot 3 - 23 \cdot 4}{24} = \frac{141 - 92}{24} = \frac{49}{24} = 2\frac{1}{24}$$