Дом. Задание на 5.05 Вычислите: 1) 4 \( \frac{10}{11} \) \(\cdot\) (\( \frac{8}{9} \) - \( \frac{7}{12} \)) - 9 : 2 \( \frac{4}{7} \) 2) \( \frac{16}{15} \) \(\cdot\) \( \frac{2}{5} \) - 6 \( \frac{1}{3} \) + 2 \( \frac{1}{12} \) \(\cdot\) \( \frac{4}{5} \) 3) \( \frac{4}{3} \) + (-5 \( \frac{1}{2} \) + \( \frac{5}{4} \) \(\cdot\) 3 \( \frac{1}{5} \)) : \( \frac{9}{10} \) 4) \( \frac{14}{15} \) - \( \frac{9}{5} \) : (7 - 4 \( \frac{3}{7} \)) + \( \frac{3}{5} \) 5) \( \frac{65}{96} \) : (\( \frac{5}{16} \) - \( \frac{7}{12} \)) + 10 \(\cdot\) 1 \( \frac{3}{20} \)

Решение:

1. 1)
   
   • \( \frac{8}{9} - \frac{7}{12} = \frac{32 - 21}{36} = \frac{11}{36} \)
   • \( 4 \frac{10}{11} = \frac{54}{11} \)
   • \( 2 \frac{4}{7} = \frac{18}{7} \)
   • \( \frac{54}{11} \(\cdot\) \(\frac{11}{36}\) = \(\frac{54}{36}\) = \(\frac{3}{2}\) \)
   • \( 9 : \frac{18}{7} = 9 \(\cdot\) \(\frac{7}{18}\) = \(\frac{7}{2}\) \)
   • \( \frac{3}{2} - \frac{7}{2} = \frac{-4}{2} = -2 \)
2. 2)
   
   • \( \frac{16}{15} \(\cdot\) \(\frac{2}{5}\) = \(\frac{32}{75}\) \)
   • \( 6 \frac{1}{3} = \frac{19}{3} \)
   • \( 2 \frac{1}{12} = \frac{25}{12} \)
   • \( \frac{25}{12} \(\cdot\) \(\frac{4}{5}\) = \(\frac\){25 \(\cdot\) 4}{12 \(\cdot\) 5} = \(\frac{100}{60}\) = \(\frac{5}{3}\) \)
   • \( \frac{32}{75} - \frac{19}{3} + \frac{5}{3} = \frac{32}{75} - \frac{19 \(\cdot\) 25}{75} + \(\frac\){5 \(\cdot\) 25}{75} = \(\frac{32 - 475 + 125}{75}\) = \(\frac{-318}{75}\) = \(\frac{-106}{25}\) \)
3. 3)
   
   • \( 5 \frac{1}{2} = \frac{11}{2} \)
   • \( 3 \frac{1}{5} = \frac{16}{5} \)
   • \( \frac{5}{4} \(\cdot\) \(\frac{16}{5}\) = \(\frac\){5 \(\cdot\) 16}{4 \(\cdot\) 5} = \(\frac{80}{20}\) = 4 \)
   • \( - \frac{11}{2} + 4 = \frac{-11 + 8}{2} = - \frac{3}{2} \)
   • \( - \frac{3}{2} : \frac{9}{10} = - \frac{3}{2} \(\cdot\) \(\frac{10}{9}\) = - \(\frac\){3 \(\cdot\) 10}{2 \(\cdot\) 9} = - \(\frac{30}{18}\) = - \(\frac{5}{3}\) \)
   • \( \frac{4}{3} + ( - \frac{5}{3} ) = \frac{4-5}{3} = - \frac{1}{3} \)
4. 4)
   
   • \( 7 - 4 \frac{3}{7} = 7 - \frac{31}{7} = \frac{49 - 31}{7} = \frac{18}{7} \)
   • \( \frac{9}{5} : \frac{18}{7} = \frac{9}{5} \(\cdot\) \(\frac{7}{18}\) = \(\frac\){9 \(\cdot\) 7}{5 \(\cdot\) 18} = \(\frac{63}{90}\) = \(\frac{7}{10}\) \)
   • \( \frac{14}{15} - \frac{7}{10} + \frac{3}{5} = \frac{28 - 21 + 18}{30} = \frac{25}{30} = \frac{5}{6} \)
5. 5)
   
   • \( \frac{5}{16} - \frac{7}{12} = \frac{15 - 28}{48} = - \frac{13}{48} \)
   • \( 1 \frac{3}{20} = \frac{23}{20} \)
   • \( \frac{65}{96} : (- \frac{13}{48} ) = \frac{65}{96} \(\cdot\) \(- \frac{48}{13}\) = - \(\frac\){65 \(\cdot\) 48}{96 \(\cdot\) 13} = - \(\frac\){65 \(\cdot\) 1}{2 \(\cdot\) 13} = - \(\frac\){5 \(\cdot\) 13 \(\cdot\) 1}{2 \(\cdot\) 13} = - \(\frac{5}{2}\) \)
   • \( - \frac{5}{2} + 10 \(\cdot\) \(\frac{23}{20}\) = - \(\frac{5}{2}\) + \(\frac{23}{2}\) = \(\frac{-5 + 23}{2}\) = \(\frac{18}{2}\) = 9 \)

Ответ: 1) -2; 2) -106/25; 3) -1/3; 4) 5/6; 5) 9.