Найдите значение выражения: 1) 14 7/15 - 3 9/23 * 23/27 - 1 1/45 * 1/6

1) $14 \frac{7}{15} - 3 \frac{9}{23} \cdot \frac{23}{27} - 1 \frac{1}{45} \cdot \frac{1}{6} = 14 \frac{7}{15} - (\frac{78}{23} \cdot \frac{23}{27}) - (\frac{46}{45} \cdot \frac{1}{6}) = 14 \frac{7}{15} - \frac{78}{27} - \frac{23}{135} = 14 \frac{63}{135} - \frac{390}{135} - \frac{23}{135} = 14 \frac{63-390-23}{135} = 13 \frac{135+63-390-23}{135} = 13 \frac{-215}{135}$ — тут лучше перевести в неправильную дробь: $14 \frac{7}{15} = \frac{217}{15} = \frac{1953}{135}$. $\frac{1953 - 390 - 23}{135} = \frac{1540}{135} = \frac{308}{27} = 11 \frac{11}{27}$.\n\n2) $8 \frac{1}{3} \cdot 9 - 4 \frac{1}{3} \cdot 3 \frac{1}{4} - 2 \frac{2}{7} \cdot 3 \frac{5}{24} = (\frac{25}{3} \cdot 9) - (\frac{13}{3} \cdot \frac{13}{4}) - (\frac{16}{7} \cdot \frac{77}{24}) = 75 - \frac{169}{12} - \frac{2}{1} \cdot \frac{11}{3} = 75 - 14 \frac{1}{12} - 7 \frac{1}{3} = 75 - 14 \frac{1}{12} - 7 \frac{4}{12} = 75 - 21 \frac{5}{12} = 53 \frac{7}{12}$.\n\n3) $1 \frac{1}{48} \cdot 2 \frac{2}{5} - (9 \frac{1}{6} \cdot \frac{4}{15} + 2 \frac{5}{9}) \cdot \frac{2}{5} = (\frac{49}{48} \cdot \frac{12}{5}) - ((\frac{55}{6} \cdot \frac{4}{15}) + 2 \frac{5}{9}) \cdot \frac{2}{5} = \frac{49}{20} - ((\frac{11}{3} \cdot \frac{2}{3}) + 2 \frac{5}{9}) \cdot \frac{2}{5} = 2 \frac{9}{20} - (2 \frac{4}{9} + 2 \frac{5}{9}) \cdot \frac{2}{5} = 2 \frac{9}{20} - (4 \frac{9}{9}) \cdot \frac{2}{5} = 2 \frac{9}{20} - 5 \cdot \frac{2}{5} = 2 \frac{9}{20} - 2 = \frac{9}{20}$.\n\n4) $5 \frac{1}{8} \cdot \frac{16}{41} \cdot 5 \frac{1}{2} + (\frac{13}{17} + \frac{4}{5}) \cdot 1 \frac{2}{83} = (\frac{41}{8} \cdot \frac{16}{41} \cdot \frac{11}{2}) + (\frac{65+68}{85}) \cdot \frac{85}{83} = 11 + \frac{133}{85} \cdot \frac{85}{83} = 11 + \frac{133}{83} = 11 + 1 \frac{50}{83} = 12 \frac{50}{83}$.