Решение:

1. $$\frac{4}{15} + \frac{4}{5} = \frac{4}{15} + \frac{4 \cdot 3}{5 \cdot 3} = \frac{4}{15} + \frac{12}{15} = \frac{4+12}{15} = \frac{16}{15} = 1\frac{1}{15}$$
2. $$\frac{3}{7} - \frac{1}{21} = \frac{3 \cdot 3}{7 \cdot 3} - \frac{1}{21} = \frac{9}{21} - \frac{1}{21} = \frac{9-1}{21} = \frac{8}{21}$$
3. $$\frac{13}{18} - \frac{5}{9} = \frac{13}{18} - \frac{5 \cdot 2}{9 \cdot 2} = \frac{13}{18} - \frac{10}{18} = \frac{13-10}{18} = \frac{3}{18} = \frac{1}{6}$$
4. $$\frac{17}{24} - \frac{1}{12} = \frac{17}{24} - \frac{1 \cdot 2}{12 \cdot 2} = \frac{17}{24} - \frac{2}{24} = \frac{17-2}{24} = \frac{15}{24} = \frac{5}{8}$$
5. $$\begin{array}{r} \begin{array}{r}5,30 \\ -2,85 \end{array} \\ \hline \\ 2,45 \end{array}$$
6. $$\frac{5}{8} : 3\frac{1}{8} = \frac{5}{8} : \frac{3 \cdot 8 + 1}{8} = \frac{5}{8} : \frac{25}{8} = \frac{5}{8} \cdot \frac{8}{25} = \frac{5 \cdot 8}{8 \cdot 25} = \frac{5}{25} = \frac{1}{5}$$
7. $$\frac{1}{5} : 3\frac{1}{5} = \frac{1}{5} : \frac{3 \cdot 5 + 1}{5} = \frac{1}{5} : \frac{16}{5} = \frac{1}{5} \cdot \frac{5}{16} = \frac{1 \cdot 5}{5 \cdot 16} = \frac{1}{16}$$
8. $$\frac{1}{6} : 3\frac{1}{6} = \frac{1}{6} : \frac{3 \cdot 6 + 1}{6} = \frac{1}{6} : \frac{19}{6} = \frac{1}{6} \cdot \frac{6}{19} = \frac{1 \cdot 6}{6 \cdot 19} = \frac{1}{19}$$
9. 5% от 45 = $$45 \cdot \frac{5}{100} = 45 \cdot 0.05 = 2.25$$
10. 12% от 50 = $$50 \cdot \frac{12}{100} = 50 \cdot 0.12 = 6$$

Ответы:

1. $$1\frac{1}{15}$$
2. $$\frac{8}{21}$$
3. $$\frac{1}{6}$$
4. $$\frac{5}{8}$$
5. $$2,45$$
6. $$\frac{1}{5}$$
7. $$\frac{1}{16}$$
8. $$\frac{1}{19}$$
9. $$2.25$$
10. $$6$$