1. Найдите значение выражения: a) 2\(\frac{5}{8}\) + 1\(\frac{1}{3}\); б) 4\(\frac{4}{9}\) - 2\(\frac{5}{6}\); в) 6\(\frac{7}{12}\) + (\(\frac{5}{40}\) - 4\(\frac{8}{15}\))

Решение:

1. \( \text{а) } 2\frac{5}{8} + 1\frac{1}{3} = \frac{2 × 8 + 5}{8} + \frac{1 × 3 + 1}{3} = \frac{16+5}{8} + \frac{3+1}{3} = \frac{21}{8} + \frac{4}{3} = \frac{21 × 3 + 4 × 8}{24} = \frac{63 + 32}{24} = \frac{95}{24} = 3\frac{23}{24} \)
2. \( \text{б) } 4\frac{4}{9} - 2\frac{5}{6} = \frac{4 × 9 + 4}{9} - \frac{2 × 6 + 5}{6} = \frac{36+4}{9} - \frac{12+5}{6} = \frac{40}{9} - \frac{17}{6} = \frac{40 × 2 - 17 × 3}{18} = \frac{80 - 51}{18} = \frac{29}{18} = 1\frac{11}{18} \)
3. \( \text{в) } 6\frac{7}{12} + (\frac{5}{40} - 4\frac{8}{15}) = \frac{6 × 12 + 7}{12} + (\frac{5}{40} - \frac{4 × 15 + 8}{15}) = \frac{72+7}{12} + (\frac{1}{8} - \frac{60+8}{15}) = \frac{79}{12} + (\frac{1}{8} - \frac{68}{15}) = \frac{79}{12} + (\frac{1 × 15 - 68 × 8}{120}) = \frac{79}{12} + \frac{15 - 544}{120} = \frac{79}{12} + \frac{-529}{120} = \frac{79 × 10 - 529}{120} = \frac{790 - 529}{120} = \frac{261}{120} = \frac{87}{40} = 2\frac{7}{40} \)

Ответ: а) \(3\frac{23}{24}\); б) \(1\frac{11}{18}\); в) \(2\frac{7}{40}\).