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

Давай найдем значения выражений по порядку.

а) \(\left(\frac{3}{8} - \frac{1}{20}\right) + \frac{7}{40}\)

\[\left(\frac{3}{8} - \frac{1}{20}\right) + \frac{7}{40} = \left(\frac{3 \cdot 5}{8 \cdot 5} - \frac{1 \cdot 2}{20 \cdot 2}\right) + \frac{7}{40} = \left(\frac{15}{40} - \frac{2}{40}\right) + \frac{7}{40} = \frac{13}{40} + \frac{7}{40} = \frac{20}{40} = \frac{1}{2}\]

б) \(\frac{1}{6} + \left(\frac{3}{5} - \frac{1}{3}\right)\)

\[\frac{1}{6} + \left(\frac{3}{5} - \frac{1}{3}\right) = \frac{1}{6} + \left(\frac{3 \cdot 3}{5 \cdot 3} - \frac{1 \cdot 5}{3 \cdot 5}\right) = \frac{1}{6} + \left(\frac{9}{15} - \frac{5}{15}\right) = \frac{1}{6} + \frac{4}{15} = \frac{1 \cdot 5}{6 \cdot 5} + \frac{4 \cdot 2}{15 \cdot 2} = \frac{5}{30} + \frac{8}{30} = \frac{13}{30}\]

в) \(\frac{8}{9} - \left(\frac{1}{10} + \frac{2}{5}\right)\)

\[\frac{8}{9} - \left(\frac{1}{10} + \frac{2}{5}\right) = \frac{8}{9} - \left(\frac{1}{10} + \frac{2 \cdot 2}{5 \cdot 2}\right) = \frac{8}{9} - \left(\frac{1}{10} + \frac{4}{10}\right) = \frac{8}{9} - \frac{5}{10} = \frac{8}{9} - \frac{1}{2} = \frac{8 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 9}{2 \cdot 9} = \frac{16}{18} - \frac{9}{18} = \frac{7}{18}\]

г) \(\left(\frac{5}{8} + \frac{1}{16}\right) - \frac{9}{16}\)

\[\left(\frac{5}{8} + \frac{1}{16}\right) - \frac{9}{16} = \left(\frac{5 \cdot 2}{8 \cdot 2} + \frac{1}{16}\right) - \frac{9}{16} = \left(\frac{10}{16} + \frac{1}{16}\right) - \frac{9}{16} = \frac{11}{16} - \frac{9}{16} = \frac{2}{16} = \frac{1}{8}\]

Ответ: а) \(\frac{1}{2}\); б) \(\frac{13}{30}\); в) \(\frac{7}{18}\); г) \(\frac{1}{8}\).