Решение:

1. $$\frac{1}{8} + \frac{7}{12} = \frac{1 \cdot 3}{8 \cdot 3} + \frac{7 \cdot 2}{12 \cdot 2} = \frac{3}{24} + \frac{14}{24} = \frac{3 + 14}{24} = \frac{17}{24}$$
2. $$\frac{5}{6} + \frac{3}{4} = \frac{5 \cdot 2}{6 \cdot 2} + \frac{3 \cdot 3}{4 \cdot 3} = \frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12} = 1 \frac{7}{12}$$
3. $$2 \frac{37}{48} = \frac{2 \cdot 48 + 37}{48} = \frac{96 + 37}{48} = \frac{133}{48} = 2 \frac{37}{48}$$
4. $$\frac{17}{22} : \frac{1}{11} = \frac{17}{22} \cdot \frac{11}{1} = \frac{17 \cdot 11}{22 \cdot 1} = \frac{17 \cdot 11}{2 \cdot 11 \cdot 1} = \frac{17}{2} = 8 \frac{1}{2}$$
5. $$6 - 4 \frac{5}{8} = 6 - \frac{4 \cdot 8 + 5}{8} = 6 - \frac{32 + 5}{8} = 6 - \frac{37}{8} = \frac{6 \cdot 8}{8} - \frac{37}{8} = \frac{48}{8} - \frac{37}{8} = \frac{48 - 37}{8} = \frac{11}{8} = 1 \frac{3}{8}$$
6. $$\frac{3}{4} - \frac{1}{6} \cdot 3 = \frac{3}{4} - \frac{1 \cdot 3}{6} = \frac{3}{4} - \frac{3}{6} = \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{1 \cdot 2}{2 \cdot 2} = \frac{3}{4} - \frac{2}{4} = \frac{3 - 2}{4} = \frac{1}{4}$$
7. $$\left( \frac{10}{13} + \frac{15}{4} \right) \cdot \frac{26}{5} = \left( \frac{10 \cdot 4}{13 \cdot 4} + \frac{15 \cdot 13}{4 \cdot 13} \right) \cdot \frac{26}{5} = \left( \frac{40}{52} + \frac{195}{52} \right) \cdot \frac{26}{5} = \frac{40 + 195}{52} \cdot \frac{26}{5} = \frac{235}{52} \cdot \frac{26}{5} = \frac{235 \cdot 26}{52 \cdot 5} = \frac{5 \cdot 47 \cdot 2 \cdot 13}{4 \cdot 13 \cdot 5} = \frac{47 \cdot 2}{4} = \frac{47}{2} = 23 \frac{1}{2}$$
8. $$1 \frac{8}{17} : \left( \frac{12}{17} + 2 \frac{7}{11} \right) = \frac{1 \cdot 17 + 8}{17} : \left( \frac{12}{17} + \frac{2 \cdot 11 + 7}{11} \right) = \frac{25}{17} : \left( \frac{12}{17} + \frac{29}{11} \right) = \frac{25}{17} : \left( \frac{12 \cdot 11}{17 \cdot 11} + \frac{29 \cdot 17}{11 \cdot 17} \right) = \frac{25}{17} : \left( \frac{132}{187} + \frac{493}{187} \right) = \frac{25}{17} : \frac{132 + 493}{187} = \frac{25}{17} : \frac{625}{187} = \frac{25}{17} \cdot \frac{187}{625} = \frac{25 \cdot 187}{17 \cdot 625} = \frac{25 \cdot 11 \cdot 17}{17 \cdot 25 \cdot 25} = \frac{11}{25}$$

Ответы:

1. $$\frac{17}{24}$$
2. $$1 \frac{7}{12}$$
3. $$2 \frac{37}{48}$$
4. $$8 \frac{1}{2}$$
5. $$1 \frac{3}{8}$$
6. $$\frac{1}{4}$$
7. $$23 \frac{1}{2}$$
8. $$\frac{11}{25}$$