5.445 Вычислите: а) \(\frac{1}{2} + \frac{1}{3}\); г) \(\frac{3}{7} + \frac{4}{9}\); ж) \(\frac{1}{6} + \frac{1}{3}\); к) \(\frac{7}{15} - \frac{3}{10}\); н) \(\frac{5}{11} + \frac{3}{5}\); б) \(\frac{1}{3} + \frac{2}{7}\); д) \(\frac{5}{9} - \frac{1}{6}\); з) \(\frac{9}{5} - \frac{7}{10}\); л) \(\frac{3}{8} + \frac{5}{12}\); о) \(\frac{17}{30} - \frac{3}{6}\); в) \(\frac{2}{5} + \frac{1}{3}\); е) \(\frac{3}{4} - \frac{1}{3}\); и) \(\frac{1}{2} - \frac{3}{8}\); м) \(\frac{5}{9} - \frac{1}{6}\); п) \(\frac{17}{35} - \frac{4}{15}\)

a) \(\frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}\)

б) \(\frac{1}{3} + \frac{2}{7} = \frac{1 \cdot 7}{3 \cdot 7} + \frac{2 \cdot 3}{7 \cdot 3} = \frac{7}{21} + \frac{6}{21} = \frac{7+6}{21} = \frac{13}{21}\)

в) \(\frac{2}{5} + \frac{1}{3} = \frac{2 \cdot 3}{5 \cdot 3} + \frac{1 \cdot 5}{3 \cdot 5} = \frac{6}{15} + \frac{5}{15} = \frac{6+5}{15} = \frac{11}{15}\)

г) \(\frac{3}{7} + \frac{4}{9} = \frac{3 \cdot 9}{7 \cdot 9} + \frac{4 \cdot 7}{9 \cdot 7} = \frac{27}{63} + \frac{28}{63} = \frac{27+28}{63} = \frac{55}{63}\)

д) \(\frac{5}{9} - \frac{1}{6} = \frac{5 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 3}{6 \cdot 3} = \frac{10}{18} - \frac{3}{18} = \frac{10-3}{18} = \frac{7}{18}\)

e) \(\frac{3}{4} - \frac{1}{3} = \frac{3 \cdot 3}{4 \cdot 3} - \frac{1 \cdot 4}{3 \cdot 4} = \frac{9}{12} - \frac{4}{12} = \frac{9-4}{12} = \frac{5}{12}\)

ж) \(\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{1}{6} + \frac{2}{6} = \frac{1+2}{6} = \frac{3}{6} = \frac{1}{2}\)

з) \(\frac{9}{5} - \frac{7}{10} = \frac{9 \cdot 2}{5 \cdot 2} - \frac{7}{10} = \frac{18}{10} - \frac{7}{10} = \frac{18-7}{10} = \frac{11}{10} = 1\frac{1}{10}\)

и) \(\frac{1}{2} - \frac{3}{8} = \frac{1 \cdot 4}{2 \cdot 4} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{4-3}{8} = \frac{1}{8}\)

к) \(\frac{7}{15} - \frac{3}{10} = \frac{7 \cdot 2}{15 \cdot 2} - \frac{3 \cdot 3}{10 \cdot 3} = \frac{14}{30} - \frac{9}{30} = \frac{14-9}{30} = \frac{5}{30} = \frac{1}{6}\)

л) \(\frac{3}{8} + \frac{5}{12} = \frac{3 \cdot 3}{8 \cdot 3} + \frac{5 \cdot 2}{12 \cdot 2} = \frac{9}{24} + \frac{10}{24} = \frac{9+10}{24} = \frac{19}{24}\)

м) \(\frac{5}{9} - \frac{1}{6} = \frac{5 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 3}{6 \cdot 3} = \frac{10}{18} - \frac{3}{18} = \frac{10-3}{18} = \frac{7}{18}\)

н) \(\frac{5}{11} + \frac{3}{5} = \frac{5 \cdot 5}{11 \cdot 5} + \frac{3 \cdot 11}{5 \cdot 11} = \frac{25}{55} + \frac{33}{55} = \frac{25+33}{55} = \frac{58}{55} = 1\frac{3}{55}\)

о) \(\frac{17}{30} - \frac{3}{6} = \frac{17}{30} - \frac{3 \cdot 5}{6 \cdot 5} = \frac{17}{30} - \frac{15}{30} = \frac{17-15}{30} = \frac{2}{30} = \frac{1}{15}\)

п) \(\frac{17}{35} - \frac{4}{15} = \frac{17 \cdot 3}{35 \cdot 3} - \frac{4 \cdot 7}{15 \cdot 7} = \frac{51}{105} - \frac{28}{105} = \frac{51-28}{105} = \frac{23}{105}\)

Ответ: а) \(\frac{5}{6}\); б) \(\frac{13}{21}\); в) \(\frac{11}{15}\); г) \(\frac{55}{63}\); д) \(\frac{7}{18}\); е) \(\frac{5}{12}\); ж) \(\frac{1}{2}\); з) \(1\frac{1}{10}\); и) \(\frac{1}{8}\); к) \(\frac{1}{6}\); л) \(\frac{19}{24}\); м) \(\frac{7}{18}\); н) \(1\frac{3}{55}\); о) \(\frac{1}{15}\); п) \(\frac{23}{105}\)