Найдите значение выражения: 1) (\frac{17}{15}-\frac{1}{12}) \cdot \frac{20}{3}; 2) \frac{8}{9}+\frac{7}{12}\cdot\frac{4}{21}; 3) 3\frac{11}{15}:\frac{5}{3}+\frac{1}{3}; 4) (\frac{2}{5}+\frac{3}{4}):\frac{23}{20}; 5) \frac{5}{12}:(\frac{7}{16}-\frac{1}{8}); 6) \frac{47}{7}:\frac{15}{56}\cdot\frac{3}{8}; 7) 1\frac{1}{3}+\frac{5}{11}-\frac{23}{33}; 8) 1-\frac{2}{5}\cdot2\frac{1}{7}

Ответ: 1) 3; 2) \frac{7}{9}; 3) 4\frac{1}{5}; 4) 1; 5) 3\frac{1}{3}; 6) 7\frac{5}{12}; 7) \frac{5}{3}; 8) \frac{24}{35}

1. \(\frac{17}{15}-\frac{1}{12}) \cdot \frac{20}{3} = (\frac{17 \cdot 4}{15 \cdot 4}-\frac{1 \cdot 5}{12 \cdot 5}) \cdot \frac{20}{3} = (\frac{68}{60}-\frac{5}{60}) \cdot \frac{20}{3} = \frac{63}{60} \cdot \frac{20}{3} = \frac{63 \cdot 20}{60 \cdot 3} = \frac{63}{9} = 7 \)
   Ответ: 7
2. \(\frac{8}{9}+\frac{7}{12}\cdot\frac{4}{21} = \frac{8}{9}+\frac{7 \cdot 4}{12 \cdot 21} = \frac{8}{9}+\frac{1}{9} = \frac{9}{9} = 1\)
   Ответ: 1
3. \(3\frac{11}{15}:\frac{5}{3}+\frac{1}{3} = \frac{56}{15}:\frac{5}{3}+\frac{1}{3} = \frac{56}{15} \cdot \frac{3}{5}+\frac{1}{3} = \frac{56 \cdot 3}{15 \cdot 5} + \frac{1}{3} = \frac{56}{25} + \frac{1}{3} = \frac{56 \cdot 3}{25 \cdot 3} + \frac{1 \cdot 25}{3 \cdot 25} = \frac{168}{75} + \frac{25}{75} = \frac{193}{75} = 2\frac{43}{75}\)
   Ответ: 2\frac{43}{75}
4. \((\frac{2}{5}+\frac{3}{4}):\frac{23}{20} = (\frac{2 \cdot 4}{5 \cdot 4}+\frac{3 \cdot 5}{4 \cdot 5}):\frac{23}{20} = (\frac{8}{20}+\frac{15}{20}):\frac{23}{20} = \frac{23}{20}:\frac{23}{20} = 1\)
   Ответ: 1
5. \(\frac{5}{12}:(\frac{7}{16}-\frac{1}{8}) = \frac{5}{12}:(\frac{7}{16}-\frac{1 \cdot 2}{8 \cdot 2}) = \frac{5}{12}:(\frac{7}{16}-\frac{2}{16}) = \frac{5}{12}:\frac{5}{16} = \frac{5}{12} \cdot \frac{16}{5} = \frac{16}{12} = 1\frac{4}{12} = 1\frac{1}{3}\)
   Ответ: 1\frac{1}{3}
6. \(\frac{47}{7}:\frac{15}{56}\cdot\frac{3}{8} = \frac{47}{7} \cdot \frac{56}{15} \cdot \frac{3}{8} = \frac{47 \cdot 56 \cdot 3}{7 \cdot 15 \cdot 8} = \frac{47 \cdot 8 \cdot 3}{15 \cdot 8} = \frac{47 \cdot 3}{15} = \frac{141}{15} = 9\frac{6}{15} = 9\frac{2}{5}\)
   Ответ: 9\frac{2}{5}
7. \(1\frac{1}{3}+\frac{5}{11}-\frac{23}{33} = \frac{4}{3}+\frac{5}{11}-\frac{23}{33} = \frac{4 \cdot 11}{3 \cdot 11}+\frac{5 \cdot 3}{11 \cdot 3}-\frac{23}{33} = \frac{44}{33}+\frac{15}{33}-\frac{23}{33} = \frac{36}{33} = \frac{12}{11} = 1\frac{1}{11}\)
   Ответ: 1\frac{1}{11}
8. \(1-\frac{2}{5}\cdot2\frac{1}{7} = 1 - \frac{2}{5} \cdot \frac{15}{7} = 1 - \frac{2 \cdot 15}{5 \cdot 7} = 1 - \frac{2 \cdot 3}{7} = 1 - \frac{6}{7} = \frac{1}{7}\)
   Ответ: \frac{1}{7}

Ответ: 1) 7; 2) 1; 3) 2\frac{43}{75}; 4) 1; 5) 1\frac{1}{3}; 6) 9\frac{2}{5}; 7) 1\frac{1}{11}; 8) \frac{1}{7}