2.276 Выполните действия: a) \(\frac{4}{9} + \frac{5}{12}\) \(\frac{18}{31}\); б) \(\frac{6}{25} \cdot (\frac{11}{15} - \frac{9}{20})\); в) \((4 - \frac{3}{15}) \cdot \frac{5}{8}\); г) \((5 - 4\frac{1}{7}) \cdot (7\frac{1}{6} - 6\frac{5}{12});\) д) \((1\frac{1}{24} - \frac{5}{12}) \cdot (4\frac{1}{8} - 3\frac{5}{24});\) e) \((1\frac{2}{15} - \frac{11}{15}) \cdot (5\frac{3}{18} - 4\frac{1}{27});\)

a) \(\frac{4}{9} + \frac{5}{12}\) \(\frac{18}{31}\) = \(\frac{4 \cdot 4 + 5 \cdot 3}{36}\) \(\frac{18}{31}\) = \(\frac{16 + 15}{36} \cdot \frac{18}{31}\) = \(\frac{31}{36} \cdot \frac{18}{31}\) = \(\frac{1}{2}\)

Ответ: \(\frac{1}{2}\)

б) \(\frac{6}{25} \cdot (\frac{11}{15} - \frac{9}{20})\) = \(\frac{6}{25} \cdot \frac{11 \cdot 4 - 9 \cdot 3}{60}\) = \(\frac{6}{25} \cdot \frac{44 - 27}{60}\) = \(\frac{6}{25} \cdot \frac{17}{60}\) = \(\frac{1}{25} \cdot \frac{17}{10}\) = \(\frac{17}{250}\)

Ответ: \(\frac{17}{250}\)

в) \((4 - \frac{3}{15}) \cdot \frac{5}{8}\) = \((4 - \frac{1}{5}) \cdot \frac{5}{8}\) = \((\frac{20 - 1}{5}) \cdot \frac{5}{8}\) = \(\frac{19}{5} \cdot \frac{5}{8}\) = \(\frac{19}{8}\) = 2\(\frac{3}{8}\)

Ответ: 2\(\frac{3}{8}\)

г) \((5 - 4\frac{1}{7}) \cdot (7\frac{1}{6} - 6\frac{5}{12});\) = \((5 - \frac{29}{7}) \cdot (\frac{43}{6} - \frac{77}{12});\) = \((\frac{35 - 29}{7}) \cdot (\frac{43 \cdot 2 - 77}{12});\) = \((\frac{6}{7}) \cdot (\frac{86 - 77}{12});\) = \(\frac{6}{7} \cdot \frac{9}{12}\) = \(\frac{6}{7} \cdot \frac{3}{4}\) = \(\frac{3}{7} \cdot \frac{3}{2}\) = \(\frac{9}{14}\)

Ответ: \(\frac{9}{14}\)

д) \((1\frac{1}{24} - \frac{5}{12}) \cdot (4\frac{1}{8} - 3\frac{5}{24});\) = \((\frac{25}{24} - \frac{10}{24}) \cdot (\frac{33}{8} - \frac{77}{24});\) = \(\frac{15}{24} \cdot \frac{99 - 77}{24};\) = \(\frac{15}{24} \cdot \frac{22}{24}\) = \(\frac{5}{8} \cdot \frac{11}{12}\) = \(\frac{55}{96}\)

Ответ: \(\frac{55}{96}\)

e) \((1\frac{2}{15} - \frac{11}{15}) \cdot (5\frac{3}{18} - 4\frac{1}{27});\) = \((\frac{17}{15} - \frac{11}{15}) \cdot (\frac{93}{18} - \frac{109}{27});\) = \(\frac{6}{15} \cdot (\frac{93 \cdot 3 - 109 \cdot 2}{54});\) = \(\frac{2}{5} \cdot (\frac{279 - 218}{54});\) = \(\frac{2}{5} \cdot \frac{61}{54}\) = \(\frac{1}{5} \cdot \frac{61}{27}\) = \(\frac{61}{135}\)

Ответ: \(\frac{61}{135}\)