Найдите значение выражения: 1) (\frac{13}{10}-\frac{5}{6}) \cdot \frac{30}{7}; 2) \frac{13}{15}+\frac{5}{18}:\frac{12}{25}; 3) \frac{9}{14}:2\frac{5}{4}-\frac{4}{35}; 4) (\frac{3}{5}+\frac{2}{3}):\frac{19}{7}; 5) \frac{6}{5}:(\frac{9}{10}-\frac{1}{5}); 6) \frac{21}{8}:\frac{4}{3}\cdot\frac{7}{6}; 7) 1\frac{3}{4}+\frac{5}{8}-\frac{29}{32}; 8) 2-\frac{5}{8}\cdot2\frac{2}{3}

Ответ: 1) 3; 2) 1\frac{113}{180}; 3) -\frac{1}{10}; 4) \frac{3}{5}; 5) 2; 6) 2\frac{23}{32}; 7) 1\frac{31}{32}; 8) \frac{5}{3}

1. \((\frac{13}{10}-\frac{5}{6}) \cdot \frac{30}{7} = (\frac{13 \cdot 3}{10 \cdot 3}-\frac{5 \cdot 5}{6 \cdot 5}) \cdot \frac{30}{7} = (\frac{39}{30}-\frac{25}{30}) \cdot \frac{30}{7} = \frac{14}{30} \cdot \frac{30}{7} = \frac{14 \cdot 30}{30 \cdot 7} = \frac{14}{7} = 2\)
   Ответ: 2
2. \(\frac{13}{15}+\frac{5}{18}:\frac{12}{25} = \frac{13}{15}+\frac{5}{18} \cdot \frac{25}{12} = \frac{13}{15}+\frac{5 \cdot 25}{18 \cdot 12} = \frac{13}{15} + \frac{125}{216} = \frac{13 \cdot 72}{15 \cdot 72} + \frac{125 \cdot 5}{216 \cdot 5} = \frac{936}{1080} + \frac{625}{1080} = \frac{1561}{1080} = 1\frac{481}{1080}\)
   Ответ: 1\frac{481}{1080}
3. \(\frac{9}{14}:2\frac{5}{4}-\frac{4}{35} = \frac{9}{14}:\frac{13}{4}-\frac{4}{35} = \frac{9}{14} \cdot \frac{4}{13}-\frac{4}{35} = \frac{9 \cdot 4}{14 \cdot 13}-\frac{4}{35} = \frac{36}{182} - \frac{4}{35} = \frac{36 \cdot 35}{182 \cdot 35} - \frac{4 \cdot 182}{35 \cdot 182} = \frac{1260}{6370} - \frac{728}{6370} = \frac{532}{6370} = \frac{266}{3185}\)
   Ответ: \frac{266}{3185}
4. \((\frac{3}{5}+\frac{2}{3}):\frac{19}{7} = (\frac{3 \cdot 3}{5 \cdot 3}+\frac{2 \cdot 5}{3 \cdot 5}):\frac{19}{7} = (\frac{9}{15}+\frac{10}{15}):\frac{19}{7} = \frac{19}{15}:\frac{19}{7} = \frac{19}{15} \cdot \frac{7}{19} = \frac{7}{15}\)
   Ответ: \frac{7}{15}
5. \(\frac{6}{5}:(\frac{9}{10}-\frac{1}{5}) = \frac{6}{5}:(\frac{9}{10}-\frac{1 \cdot 2}{5 \cdot 2}) = \frac{6}{5}:(\frac{9}{10}-\frac{2}{10}) = \frac{6}{5}:\frac{7}{10} = \frac{6}{5} \cdot \frac{10}{7} = \frac{6 \cdot 10}{5 \cdot 7} = \frac{6 \cdot 2}{7} = \frac{12}{7} = 1\frac{5}{7}\)
   Ответ: 1\frac{5}{7}
6. \(\frac{21}{8}:\frac{4}{3}\cdot\frac{7}{6} = \frac{21}{8} \cdot \frac{3}{4} \cdot \frac{7}{6} = \frac{21 \cdot 3 \cdot 7}{8 \cdot 4 \cdot 6} = \frac{441}{192} = 2\frac{57}{192} = 2\frac{19}{64}\)
   Ответ: 2\frac{19}{64}
7. \(1\frac{3}{4}+\frac{5}{8}-\frac{29}{32} = \frac{7}{4}+\frac{5}{8}-\frac{29}{32} = \frac{7 \cdot 8}{4 \cdot 8}+\frac{5 \cdot 4}{8 \cdot 4}-\frac{29}{32} = \frac{56}{32}+\frac{20}{32}-\frac{29}{32} = \frac{47}{32} = 1\frac{15}{32}\)
   Ответ: 1\frac{15}{32}
8. \(2-\frac{5}{8}\cdot2\frac{2}{3} = 2 - \frac{5}{8} \cdot \frac{8}{3} = 2 - \frac{5 \cdot 8}{8 \cdot 3} = 2 - \frac{5}{3} = \frac{1}{3}\)
   Ответ: \frac{1}{3}

Ответ: 1) 2; 2) 1\frac{481}{1080}; 3) \frac{266}{3185}; 4) \frac{7}{15}; 5) 1\frac{5}{7}; 6) 2\frac{19}{64}; 7) 1\frac{15}{32}; 8) \frac{1}{3}