Решение:
а) $\frac{4}{15} + \frac{5}{36} + \frac{11}{15} + \frac{31}{36} = (\frac{4}{15} + \frac{11}{15}) + (\frac{5}{36} + \frac{31}{36}) = \frac{15}{15} + \frac{36}{36} = 1 + 1 = 2$;
б) $\frac{7}{25} + \frac{32}{33} - \frac{7}{25} = (\frac{7}{25} - \frac{7}{25}) + \frac{32}{33} = 0 + \frac{32}{33} = \frac{32}{33}$;
в) $\frac{39}{40} * \frac{124}{125} : \frac{124}{125} = \frac{39}{40} * \frac{\overset{1}{\cancel{124}}}{\underset{1}{\cancel{125}}} * \frac{\overset{1}{\cancel{125}}}{\underset{1}{\cancel{125}}} = \frac{39}{40} * 1 = \frac{39}{40}$;
г) $\frac{4}{35} * \frac{17}{18} + \frac{17}{18} * \frac{31}{35} = \frac{17}{18} * (\frac{4}{35} + \frac{31}{35}) = \frac{17}{18} * \frac{35}{35} = \frac{17}{18} * 1 = \frac{17}{18}$;
д) $\frac{45}{46} * \frac{49}{51} - \frac{45}{46} * \frac{3}{51} = \frac{45}{46} * (\frac{49}{51} - \frac{3}{51}) = \frac{45}{46} * \frac{46}{51} = \frac{\overset{15}{\cancel{45}} * \overset{1}{\cancel{46}}}{\underset{1}{\cancel{46}} * \underset{17}{\cancel{51}}} = \frac{15 * 1}{1 * 17} = \frac{15}{17}$;
е) $\frac{72}{73} * \frac{34}{65} + \frac{72}{73} * \frac{39}{65} = \frac{72}{73} * (\frac{34}{65} + \frac{39}{65}) = \frac{72}{73} * \frac{73}{65} = \frac{72 * \overset{1}{\cancel{73}}}{\underset{1}{\cancel{73}} * 65} = \frac{72 * 1}{1 * 65} = \frac{72}{65} = 1\frac{7}{65}$.
Ответ:
а) $2$;
б) $\frac{32}{33}$;
в) $\frac{39}{40}$;
г) $\frac{17}{18}$;
д) $\frac{15}{17}$;
е) $1\frac{7}{65}$.