Вариант 4. Выполните действия:

Решение:

1. \(5 \frac{1}{3} \cdot 2 \frac{1}{4} : \frac{1}{5} = \frac{16}{3} \cdot \frac{9}{4} : \frac{1}{5} = \frac{16 € 9}{3 € 4} : \frac{1}{5} = 12 : \frac{1}{5} = 12 \cdot 5 = 60\)
2. \(2 \frac{2}{5} : \left( 3 \frac{2}{5} - 1 \frac{11}{15} \right) = \frac{12}{5} : \left( \frac{17}{5} - \frac{26}{15} \right) = \frac{12}{5} : \left( \frac{51}{15} - \frac{26}{15} \right) = \frac{12}{5} : \frac{25}{15} = \frac{12}{5} : \frac{5}{3} = \frac{12}{5} \cdot \frac{3}{5} = \frac{36}{25}\)
3. \(1 \frac{4}{11} \cdot 3 \frac{3}{7} : \frac{4}{7} = \frac{15}{11} \cdot \frac{24}{7} : \frac{4}{7} = \frac{15 \u0080 24}{11 € 7} : \frac{4}{7} = \frac{360}{77} : \frac{4}{7} = \frac{360}{77} \cdot \frac{7}{4} = \frac{360}{11 € 4} = \frac{90}{11}\)
4. \(\frac{8}{9} : \left( 3 \frac{1}{6} - 1 \frac{3}{4} \right) = \frac{8}{9} : \left( \frac{19}{6} - \frac{7}{4} \right) = \frac{8}{9} : \left( \frac{38}{12} - \frac{21}{12} \right) = \frac{8}{9} : \frac{17}{12} = \frac{8}{9} \cdot \frac{12}{17} = \frac{8 € 12}{9 € 17} = \frac{8 € 4}{3 € 17} = \frac{32}{51}\)
5. \(6 \frac{3}{8} \cdot 1 \frac{7}{17} - 2 \frac{3}{8} : 1 \frac{1}{4} + \frac{2}{5} = \frac{51}{8} \cdot \frac{24}{17} - \frac{19}{8} : \frac{5}{4} + \frac{2}{5} = \frac{51 € 24}{8 € 17} - \frac{19}{8} \cdot \frac{4}{5} + \frac{2}{5} = 9 - \frac{19 € 4}{8 € 5} + \frac{2}{5} = 9 - \frac{19}{10} + \frac{4}{10} = 9 - \frac{15}{10} = 9 - 1.5 = 7.5\)
6. \(10 - 2 \frac{1}{2} \cdot 3 \frac{3}{4} + \left( 2 \frac{1}{2} - 1 \frac{1}{3} \right) \cdot 6 = 10 - \frac{5}{2} \cdot \frac{15}{4} + \left( \frac{5}{2} - \frac{4}{3} \right) \cdot 6 = 10 - \frac{75}{8} + \left( \frac{15}{6} - \frac{8}{6} \right) \cdot 6 = 10 - \frac{75}{8} + \frac{7}{6} \cdot 6 = 10 - 9.375 + 7 = 17 - 9.375 = 7.625\)

Ответ:
а) \(60\)
б) \(\frac{36}{25}\)
б) \(\frac{90}{11}\)
г) \(\frac{32}{51}\)
д) \(7.5\)
е) \(7.625\)