Вычислите: 1) \(4\frac{1}{7}\cdot14-1\frac{1}{4}\cdot1\frac{1}{6}-1\frac{2}{9}\cdot2\frac{5}{8}\); 2) \(1\frac{31}{32}\cdot3\frac{1}{5}+(8\frac{5}{9}:\frac{6}{35}+3\frac{8}{15})\cdot\frac{7}{50}\); 3) \(1\frac{5}{12}\cdot2+4\cdot1\frac{1}{18}+1\frac{1}{9}\cdot1\frac{1}{4}\); 4) \(2\frac{1}{10}\cdot4\frac{1}{6}+5\cdot\frac{3}{8}-\frac{9}{20}\cdot6\); 5) \(3\cdot2\frac{7}{15}-5\frac{1}{2}\cdot\frac{7}{9}+1\frac{7}{48}\cdot2\frac{2}{11}-\frac{2}{5}\cdot6\frac{5}{9}\); 6) \((6\frac{7}{12}-3\frac{17}{36})\cdot\frac{1}{2}+4\frac{1}{3}:\frac{13}{20}\); 7) \((1\frac{11}{24}+\frac{13}{36})\cdot1\frac{11}{25}-\frac{8}{15}\cdot\frac{9}{16}\); 8) \(2\frac{1}{2}\cdot48-3\frac{2}{3}:\frac{1}{18}+5\frac{5}{12}:\frac{7}{36}\); 9) \(10\frac{5}{9}-1\frac{7}{32}\cdot(4\frac{14}{15}+3\frac{1}{15})\).

1. \(4\frac17\cdot14=\frac{29}{7}\cdot14=58\); \(1\frac14\cdot1\frac16=\frac54\cdot\frac76=\frac{35}{24}\); \(1\frac29\cdot2\frac58=\frac{11}{9}\cdot\frac{21}{8}=\frac{77}{24}\). Поэтому \(58-\frac{35}{24}-\frac{77}{24}=58-\frac{112}{24}=\frac{164}{3}=54\frac23\).
2. \(1\frac{31}{32}\cdot3\frac15=\frac{63}{32}\cdot\frac{16}{5}=\frac{63}{10}\). Далее \(8\frac59:\frac6{35}=\frac{77}{9}\cdot\frac{35}{6}=\frac{2695}{54}\), поэтому скобки дают \(\frac{2695}{54}+\frac{53}{15}=\frac{10709}{270}\). Умножая на \(\frac7{50}\) и складывая, получаем \(\frac{63}{10}+\frac{10709}{270}\cdot\frac7{50}=\frac{128177}{1350}=95\frac{107}{1350}\).
3. \(1\frac5{12}\cdot2=\frac{29}{6}\); \(4\cdot1\frac1{18}=\frac{38}{9}\); \(1\frac19\cdot1\frac14=\frac{10}{9}\). Сумма: \(\frac{29}{6}+\frac{38}{9}+\frac{10}{9}=\frac{155}{18}=8\frac{11}{18}\).
4. \(2\frac1{10}\cdot4\frac16=\frac{21}{10}\cdot\frac{25}{6}=\frac{35}{4}\), \(5\cdot\frac38=\frac{15}{8}\), \(\frac9{20}\cdot6=\frac{27}{10}\). Получаем \(\frac{35}{4}+\frac{15}{8}-\frac{27}{10}=\frac{241}{40}=6\frac1{40}\).
5. \(3\cdot2\frac7{15}=\frac{37}{5}\); \(5\frac12\cdot\frac79=\frac{77}{18}\); \(1\frac7{48}\cdot2\frac2{11}=\frac{55}{48}\cdot\frac{24}{11}=\frac52\); \(\frac25\cdot6\frac59=\frac25\cdot\frac{59}{9}=\frac{118}{45}\). Итог: \(\frac{37}{5}-\frac{77}{18}+\frac52-\frac{118}{45}=\frac{31}{90}\).
6. \(6\frac7{12}-3\frac{17}{36}=\frac{235}{36}-\frac{125}{36}=\frac{55}{18}\), после умножения на \(\frac12\) получаем \(\frac{55}{36}\). Также \(4\frac13:\frac{13}{20}=\frac{13}{3}\cdot\frac{20}{13}=\frac{20}{3}\). Сумма \(\frac{55}{36}+\frac{240}{36}=\frac{295}{36}=8\frac7{36}\).
7. \(1\frac{11}{24}+\frac{13}{36}=\frac{73}{36}\); \(1\frac{11}{25}=\frac{36}{25}\), произведение равно \(\frac{73}{25}\). Второе произведение: \(\frac8{15}\cdot\frac9{16}=\frac3{10}\). Разность \(\frac{73}{25}-\frac3{10}=\frac{131}{50}=2\frac{31}{50}\).
8. \(2\frac12\cdot48=120\); \(3\frac23:\frac1{18}=\frac{11}{3}\cdot18=66\); \(5\frac5{12}:\frac7{36}=\frac{65}{12}\cdot\frac{36}{7}=\frac{195}{7}\). Итог \(120-66+\frac{195}{7}=\frac{573}{7}=81\frac6{7}\).
9. В скобках: \(4\frac{14}{15}+3\frac1{15}=8\). Поэтому \(10\frac59-1\frac7{32}\cdot8=\frac{95}{9}-\frac{39}{32}\cdot8=\frac{95}{9}-\frac{39}{4}=\frac{29}{36}\).

Ответ: 1) \(54\frac23\); 2) \(95\frac{107}{1350}\); 3) \(8\frac{11}{18}\); 4) \(6\frac1{40}\); 5) \(\frac{31}{90}\); 6) \(8\frac7{36}\); 7) \(2\frac{31}{50}\); 8) \(81\frac67\); 9) \(\frac{29}{36}\).