Here are the solutions to the given problems:

### 1.21. Tính:

a) \(\frac{3}{4} + \frac{-1}{8}\)

To add these fractions, find a common denominator:
\[
\frac{3}{4} = \frac{6}{8}
\]
\[
\frac{6}{8} + \frac{-1}{8} = \frac{6 - 1}{8} = \frac{5}{8}
\]

b) \(\frac{-5}{12} + \frac{-7}{24}\)

Find a common denominator:
\[
\frac{-5}{12} = \frac{-10}{24}
\]
\[
\frac{-10}{24} + \frac{-7}{24} = \frac{-10 - 7}{24} = \frac{-17}{24}
\]

c) \(1 + \frac{-7}{8}\)

Convert 1 to a fraction with a denominator of 8:
\[
1 = \frac{8}{8}
\]
\[
\frac{8}{8} + \frac{-7}{8} = \frac{8 - 7}{8} = \frac{1}{8}
\]

d) \(\frac{13}{30} - \frac{1}{3}\)

Find a common denominator:
\[
\frac{1}{3} = \frac{10}{30}
\]
\[
\frac{13}{30} - \frac{10}{30} = \frac{13 - 10}{30} = \frac{3}{30} = \frac{1}{10}
\]

e) \(\frac{4}{21} - \frac{5}{28}\)

Find a common denominator:
\[
\text{LCM of 21 and 28 is 84}
\]
\[
\frac{4}{21} = \frac{16}{84}
\]
\[
\frac{5}{28} = \frac{15}{84}
\]
\[
\frac{16}{84} - \frac{15}{84} = \frac{16 - 15}{84} = \frac{1}{84}
\]

g) \(-\frac{1}{3} - 2 \frac{5}{6}\)

Convert the mixed number to an improper fraction:
\[
2 \frac{5}{6} = \frac{17}{6}
\]
Find a common denominator:
\[
\frac{-1}{3} = \frac{-2}{6}
\]
\[
\frac{-2}{6} - \frac{17}{6} = \frac{-2 - 17}{6} = \frac{-19}{6}
\]

### 1.22. Tính:

a) \(\frac{1}{3} \left(\frac{1}{2} + \frac{1}{8}\right)\)

Find a common denominator:
\[
\frac{1}{2} = \frac{4}{8}
\]
\[
\frac{4}{8} + \frac{1}{8} = \frac{5}{8}
\]
\[
\frac{1}{3} \times \frac{5}{8} = \frac{5}{24}
\]

b) \(\frac{1}{21} \left(\frac{1}{7} - \frac{1}{3}\right)\)

Find a common denominator:
\[
\frac{1}{7} = \frac{3}{21}
\]
\[
\frac{1}{3} = \frac{7}{21}
\]
\[
\frac{3}{21} - \frac{7}{21} = \frac{3 - 7}{21} = \frac{-4}{21}
\]
\[
\frac{1}{21} \times \frac{-4}{21} = \frac{-4}{441}
\]

c) \(\frac{1}{2} + \frac{1}{4} + \frac{1}{13} + \frac{1}{8}\)

Find a common denominator:
\[
\text{LCM of 2, 4, 13, and 8 is 104}
\]
\[
\frac{1}{2} = \frac{52}{104}
\]
\[
\frac{1}{4} = \frac{26}{104}
\]
\[
\frac{1}{13} = \frac{8}{104}
\]
\[
\frac{1}{8} = \frac{13}{104}
\]
\[
\frac{52}{104} + \frac{26}{104} + \frac{8}{104} + \frac{13}{104} = \frac{52 + 26 + 8 + 13}{104} = \frac{99}{104}
\]

These are the solutions to the given problems.