5.453 Найдите значение выражения: а) \((\frac{1}{3} - \frac{3}{8}) : \frac{1}{6}\) + \(\frac{7}{20} : \frac{40}{1}\); б) \((\frac{8}{9} - \frac{1}{10}) : \frac{5}{8}\) + 2\(\frac{1}{5}\) : \(\frac{9}{16}\);

a)

$$\left(\frac{1}{3} - \frac{3}{8}\right) : \frac{1}{6} + \frac{7}{20} : \frac{40}{1} = \left(\frac{8 - 9}{24}\right) : \frac{1}{6} + \frac{7}{20} \cdot \frac{1}{40} = \frac{-1}{24} \cdot 6 + \frac{7}{800} = \frac{-1}{4} + \frac{7}{800} = \frac{-200 + 7}{800} = \frac{-193}{800} = -0.24125$$

б)

$$\left(\frac{8}{9} - \frac{1}{10}\right) : \frac{5}{8} + 2\frac{1}{5} : \frac{9}{16} = \left(\frac{80 - 9}{90}\right) : \frac{5}{8} + \frac{11}{5} \cdot \frac{16}{9} = \frac{71}{90} \cdot \frac{8}{5} + \frac{176}{45} = \frac{568}{450} + \frac{176}{45} = \frac{284}{225} + \frac{880}{225} = \frac{1164}{225} = \frac{388}{75} = 5 \frac{13}{75}$$

Ответ: а) -0.24125; б) 5 \(\frac{13}{75}\)