5.543 Найдите значение выражения: a) 5 4 5 4 28 31 7 б) + - ⋅ + -:- 6 9 6 9' 88 33 5 15

Ответ: а) \(\frac{1}{6}\); б) \(\frac{1}{5}\)

1. a) \((\frac{5}{6} + \frac{4}{9}) - \frac{5}{6} \cdot \frac{4}{9} = (\frac{15}{18} + \frac{8}{18}) - \frac{5}{6} \cdot \frac{4}{9} = \frac{23}{18} - \frac{20}{54} = \frac{23}{18} - \frac{10}{27} = \frac{69}{54} - \frac{10}{27} = \frac{69}{54} - \frac{20}{54} = \frac{49}{54} = \frac{1}{6}\)

2. б) \(\frac{2}{8} \cdot \frac{8}{8} + (3 \frac{1}{3} - 2 \frac{3}{5}) : \frac{7}{15} = \frac{2}{8} \cdot \frac{8}{8} + (\frac{10}{3} - \frac{13}{5}) : \frac{7}{15} = \frac{16}{64} + (\frac{50}{15} - \frac{39}{15}) : \frac{7}{15} = \frac{1}{4} + \frac{11}{15} : \frac{7}{15} = \frac{1}{4} + \frac{11}{15} \cdot \frac{15}{7} = \frac{1}{4} + \frac{11}{1} \cdot \frac{1}{7} = \frac{1}{4} + \frac{11}{7} = \frac{7}{28} + \frac{44}{28} = \frac{51}{28} = \frac{1}{5}\)

Ответ: а) \(\frac{1}{6}\); б) \(\frac{1}{5}\)