5.543 Найдите значение выражения: a) (5/6 + 4/9 - 5/6) ⋅ 4/9; б) 2/8 : 8/8 + (3 1/3 - 2 3/5) : 7/15.

а)

\[ \left(\frac{5}{6} + \frac{4}{9} - \frac{5}{6}\right) \cdot \frac{4}{9} = \left(\frac{5}{6} - \frac{5}{6} + \frac{4}{9}\right) \cdot \frac{4}{9} = \frac{4}{9} \cdot \frac{4}{9} = \frac{4 \cdot 4}{9 \cdot 9} = \frac{16}{81} \]

Ответ: 16/81

б)

\[ \frac{2}{8} : \frac{8}{8} + \left(3\frac{1}{3} - 2\frac{3}{5}\right) : \frac{7}{15} = \frac{2}{8} : 1 + \left(\frac{10}{3} - \frac{13}{5}\right) : \frac{7}{15} = \frac{1}{4} + \left(\frac{50}{15} - \frac{39}{15}\right) : \frac{7}{15} = \frac{1}{4} + \frac{11}{15} : \frac{7}{15} = \frac{1}{4} + \frac{11}{15} \cdot \frac{15}{7} = \frac{1}{4} + \frac{11 \cdot 15}{15 \cdot 7} = \frac{1}{4} + \frac{11}{7} = \frac{7}{28} + \frac{44}{28} = \frac{51}{28} = 1\frac{23}{28} \]

Ответ: 1 23/28