1. Вычислите:

a) $$\frac{7}{13} + \frac{1}{13} = \frac{7+1}{13} = \frac{8}{13}$$

б) $$\frac{3}{10} + \frac{1}{7} = \frac{3 \cdot 7 + 1 \cdot 10}{10 \cdot 7} = \frac{21 + 10}{70} = \frac{31}{70}$$

в) $$\frac{9}{25} + \frac{2}{5} = \frac{9}{25} + \frac{2 \cdot 5}{5 \cdot 5} = \frac{9}{25} + \frac{10}{25} = \frac{9+10}{25} = \frac{19}{25}$$

г) $$\frac{1}{25} + \frac{3}{35} = \frac{1 \cdot 7 + 3 \cdot 5}{25 \cdot 7} = \frac{7+15}{175} = \frac{22}{175}$$

д) $$\frac{5}{7} - \frac{2}{7} = \frac{5-2}{7} = \frac{3}{7}$$

e) $$\frac{7}{9} - \frac{1}{4} = \frac{7 \cdot 4 - 1 \cdot 9}{9 \cdot 4} = \frac{28 - 9}{36} = \frac{19}{36}$$

ж) $$\frac{7}{8} - \frac{5}{7} = \frac{7 \cdot 7 - 5 \cdot 8}{8 \cdot 7} = \frac{49 - 40}{56} = \frac{9}{56}$$

з) $$\frac{7}{24} - \frac{7}{36} = \frac{7 \cdot 3 - 7 \cdot 2}{72} = \frac{21-14}{72} = \frac{7}{72}$$

2. Вычислите:

a) $$\frac{1}{18} + (\frac{5}{18} + \frac{1}{3}) = \frac{1}{18} + (\frac{5}{18} + \frac{1 \cdot 6}{3 \cdot 6}) = \frac{1}{18} + \frac{5+6}{18} = \frac{1}{18} + \frac{11}{18} = \frac{1+11}{18} = \frac{12}{18} = \frac{2}{3}$$

б) $$\frac{4}{15} + \frac{7}{24} + \frac{5}{24} + \frac{1}{15} = \frac{4+1}{15} + \frac{7+5}{24} = \frac{5}{15} + \frac{12}{24} = \frac{1}{3} + \frac{1}{2} = \frac{2 + 3}{6} = \frac{5}{6}$$

в) $$\frac{5}{7} + \frac{4}{5} - \frac{23}{35} = \frac{5 \cdot 5 + 4 \cdot 7 - 23}{35} = \frac{25+28-23}{35} = \frac{53-23}{35} = \frac{30}{35} = \frac{6}{7}$$