2.283 Выполните действия: a) (4/9 + 5/12) * 18/31; в) (4 - 3 * 7/15) * 5/8; д) (1/24 - 5/12) * (4/8 - 3/24); б) 6/25 * (11/15 - 9/20); г) (5 - 4/7) * (7/6 - 5/12); е) (1 2/15 - 11/15) * (5 3/18 - 4 1/27).

a) \((\frac{4}{9} + \frac{5}{12}) \cdot \frac{18}{31} = (\frac{16}{36} + \frac{15}{36}) \cdot \frac{18}{31} = \frac{31}{36} \cdot \frac{18}{31} = \frac{1}{2}\) б) \(\frac{6}{25} \cdot (\frac{11}{15} - \frac{9}{20}) = \frac{6}{25} \cdot (\frac{44}{60} - \frac{27}{60}) = \frac{6}{25} \cdot \frac{17}{60} = \frac{102}{1500} = \frac{17}{250}\) в) \((4 - 3 \cdot \frac{7}{15}) \cdot \frac{5}{8} = (4 - \frac{7}{5}) \cdot \frac{5}{8} = (\frac{20}{5} - \frac{7}{5}) \cdot \frac{5}{8} = \frac{13}{5} \cdot \frac{5}{8} = \frac{13}{8}\) д) \((\frac{1}{24} - \frac{5}{12}) \cdot (\frac{4}{8} - \frac{3}{24}) = (\frac{1}{24} - \frac{10}{24}) \cdot (\frac{12}{24} - \frac{3}{24}) = -\frac{9}{24} \cdot \frac{9}{24} = -\frac{81}{576} = -\frac{9}{64}\) г) \((5 - \frac{4}{7}) \cdot (\frac{7}{6} - \frac{5}{12}) = (\frac{35}{7} - \frac{4}{7}) \cdot (\frac{14}{12} - \frac{5}{12}) = \frac{31}{7} \cdot \frac{9}{12} = \frac{31}{7} \cdot \frac{3}{4} = \frac{93}{28}\) e) \((1 \frac{2}{15} - \frac{11}{15}) \cdot (5 \frac{3}{18} - 4 \frac{1}{27}) = (\frac{17}{15} - \frac{11}{15}) \cdot (\frac{93}{18} - \frac{109}{27}) = \frac{6}{15} \cdot (\frac{279}{54} - \frac{218}{54}) = \frac{2}{5} \cdot \frac{61}{54} = \frac{122}{270} = \frac{61}{135}\) Ответ: a) 1/2; б) 17/250; в) 13/8; д) -9/64; г) 93/28; е) 61/135