Решение:
а) $-\frac{5}{9} * (-\frac{18}{25}) - \frac{14}{27} * (-\frac{18}{35}) = \frac{\overset{1}{\cancel{5}} * \overset{2}{\cancel{18}}}{\underset{1}{\cancel{9}} * \underset{5}{\cancel{25}}} + \frac{\overset{2}{\cancel{14}} * \overset{2}{\cancel{18}}}{\underset{3}{\cancel{27}} * \underset{5}{\cancel{35}}} = \frac{1 * 2}{1 * 5} + \frac{2 * 2}{3 * 5} = \frac{2}{5} + \frac{4}{15} = \frac{6}{15} + \frac{4}{15} = \frac{6 + 4}{15} = \frac{\overset{2}{\cancel{10}}}{\underset{3}{\cancel{15}}} = \frac{2}{3}$;
б) $-\frac{27}{20} * (-\frac{5}{9}) - \frac{5}{24} * (-\frac{22}{5}) = \frac{\overset{3}{\cancel{27}} * \overset{1}{\cancel{5}}}{\underset{4}{\cancel{20}} * \underset{1}{\cancel{9}}} + \frac{\overset{1}{\cancel{5}} * \overset{11}{\cancel{22}}}{\underset{12}{\cancel{24}} * \underset{1}{\cancel{5}}} = \frac{3 * 1}{4 * 1} + \frac{1 * 11}{12 * 1} = \frac{3}{4} + \frac{11}{12} = \frac{9}{12} + \frac{11}{12} = \frac{9 + 11}{12} = \frac{\overset{5}{\cancel{20}}}{\underset{3}{\cancel{12}}} = \frac{5}{3} = 1\frac{2}{3}$;
в) $\frac{21}{20} * (-\frac{8}{21}) + \frac{7}{72} * (-\frac{36}{5}) = -\frac{\overset{1}{\cancel{21}} * \overset{2}{\cancel{8}}}{\underset{5}{\cancel{20}} * \underset{1}{\cancel{21}}} - \frac{7 * \overset{1}{\cancel{36}}}{\underset{2}{\cancel{72}} * 5} = -\frac{1 * 2}{5 * 1} - \frac{7 * 1}{2 * 5} = -\frac{2}{5} - \frac{7}{10} = -(\frac{2}{5} + \frac{7}{10}) = $ $ -(\frac{4}{10} + \frac{7}{10}) = -\frac{4 + 7}{10} = -\frac{11}{10} = -1\frac{1}{10}$;
г) $-\frac{36}{60} * (-\frac{5}{18}) - (-\frac{21}{56}) * (-\frac{1}{3}) = \frac{\overset{2}{\cancel{36}} * \overset{1}{\cancel{5}}}{\underset{12}{\cancel{60}} * \underset{1}{\cancel{18}}} - \frac{\overset{7}{\cancel{21}} * 1}{56 * \underset{1}{\cancel{3}}} = \frac{\overset{1}{\cancel{2}} * 1}{\underset{6}{\cancel{12}} * 1} - \frac{\overset{1}{\cancel{7}} * 1}{\underset{8}{\cancel{56}} * 1} = \frac{1 * 1}{6 * 1} - \frac{1 * 1}{8 * 1} = \frac{1}{6} - \frac{1}{8} = $ $ \frac{4}{24} - \frac{3}{24} = \frac{4 - 3}{24} = \frac{1}{24}$.
Ответ:
а) $\frac{2}{3}$;
б) $1\frac{2}{3}$;
в) $-1\frac{1}{10}$;
г) $\frac{1}{24}$.