5.482 Найдите значение выражения: а) \(4 + (\frac{7}{8} + \frac{3}{16})\); б) \((\frac{2}{3} + \frac{7}{8}) - (\frac{11}{24} - \frac{5}{12})\); в) \(\frac{13}{12} - \frac{12}{13} - \frac{25}{156}\).

Решение:

а) \(4 + (\frac{7}{8} + \frac{3}{16}) = 4 + (\frac{7 \cdot 2}{8 \cdot 2} + \frac{3}{16}) = 4 + (\frac{14}{16} + \frac{3}{16}) = 4 + \frac{14+3}{16} = 4 + \frac{17}{16} = 4 + 1\frac{1}{16} = 5\frac{1}{16}\)

б) \((\frac{2}{3} + \frac{7}{8}) - (\frac{11}{24} - \frac{5}{12}) = (\frac{2 \cdot 8}{3 \cdot 8} + \frac{7 \cdot 3}{8 \cdot 3}) - (\frac{11}{24} - \frac{5 \cdot 2}{12 \cdot 2}) = (\frac{16}{24} + \frac{21}{24}) - (\frac{11}{24} - \frac{10}{24}) = \frac{16+21}{24} - \frac{11-10}{24} = \frac{37}{24} - \frac{1}{24} = \frac{37-1}{24} = \frac{36}{24} = \frac{3}{2} = 1\frac{1}{2}\)

в) \(\frac{13}{12} - \frac{12}{13} - \frac{25}{156} = \frac{13 \cdot 13}{12 \cdot 13} - \frac{12 \cdot 12}{13 \cdot 12} - \frac{25}{156} = \frac{169}{156} - \frac{144}{156} - \frac{25}{156} = \frac{169-144-25}{156} = \frac{0}{156} = 0\)

Ответ: а) \(5\frac{1}{16}\); б) \(1\frac{1}{2}\); в) 0.