2.364 Выполните действия: a) $$(\frac{4}{9} + \frac{7}{36}) \cdot 36$$; б) $$(\frac{17}{18} - \frac{5}{6}) \cdot 18$$; в) $$(\frac{5}{12} + \frac{11}{18}) \cdot 36$$; г) $$(\frac{10}{11} - \frac{19}{33}) \cdot 66$$; д) $$(\frac{15}{24} + \frac{7}{36}) \cdot 12$$; e) $$(\frac{25}{26} - \frac{27}{65}) \cdot 91$$.

a) $$(\frac{4}{9} + \frac{7}{36}) \cdot 36 = (\frac{4\cdot 4}{9 \cdot 4} + \frac{7}{36}) \cdot 36 = (\frac{16}{36} + \frac{7}{36}) \cdot 36 = \frac{16+7}{36} \cdot 36 = \frac{23}{36} \cdot 36 = 23$$

б) $$(\frac{17}{18} - \frac{5}{6}) \cdot 18 = (\frac{17}{18} - \frac{5\cdot 3}{6 \cdot 3}) \cdot 18 = (\frac{17}{18} - \frac{15}{18}) \cdot 18 = \frac{17-15}{18} \cdot 18 = \frac{2}{18} \cdot 18 = 2$$

в) $$(\frac{5}{12} + \frac{11}{18}) \cdot 36 = (\frac{5\cdot 3}{12 \cdot 3} + \frac{11 \cdot 2}{18 \cdot 2}) \cdot 36 = (\frac{15}{36} + \frac{22}{36}) \cdot 36 = \frac{15+22}{36} \cdot 36 = \frac{37}{36} \cdot 36 = 37$$

г) $$(\frac{10}{11} - \frac{19}{33}) \cdot 66 = (\frac{10 \cdot 3}{11 \cdot 3} - \frac{19}{33}) \cdot 66 = (\frac{30}{33} - \frac{19}{33}) \cdot 66 = \frac{30-19}{33} \cdot 66 = \frac{11}{33} \cdot 66 = \frac{1}{3} \cdot 66 = 22$$

д) $$(\frac{15}{24} + \frac{7}{36}) \cdot 12 = (\frac{15 \cdot 3}{24 \cdot 3} + \frac{7 \cdot 2}{36 \cdot 2}) \cdot 12 = (\frac{45}{72} + \frac{14}{72}) \cdot 12 = \frac{45+14}{72} \cdot 12 = \frac{59}{72} \cdot 12 = \frac{59}{6} = 9\frac{5}{6}$$

е) $$(\frac{25}{26} - \frac{27}{65}) \cdot 91 = (\frac{25 \cdot 5}{26 \cdot 5} - \frac{27 \cdot 2}{65 \cdot 2}) \cdot 91 = (\frac{125}{130} - \frac{54}{130}) \cdot 91 = \frac{125-54}{130} \cdot 91 = \frac{71}{130} \cdot 91 = \frac{71 \cdot 7}{10} = \frac{497}{10} = 49\frac{7}{10}$$