4.283 Выполните действия

4.283 Выполните действия: а) $(3\frac{3}{16} - 5) \cdot (6\frac{26}{29} - 9)$ 1. $3\frac{3}{16} - 5 = -(5 - 3\frac{3}{16}) = -(4\frac{16}{16} - 3\frac{3}{16}) = -1\frac{13}{16} = -\frac{29}{16}$ 2. $6\frac{26}{29} - 9 = -(9 - 6\frac{26}{29}) = -(8\frac{29}{29} - 6\frac{26}{29}) = -2\frac{3}{29} = -\frac{61}{29}$ 3. $-\frac{29}{16} \cdot (-\frac{61}{29}) = \frac{29 \cdot 61}{16 \cdot 29} = \frac{61}{16} = 3\frac{13}{16} = 3,8125$ **Ответ: 3,8125** б) $11\frac{1}{5} \cdot \frac{7}{8} - 2\frac{5}{14} \cdot \frac{7}{9}$ 1. $11\frac{1}{5} \cdot \frac{7}{8} = \frac{56}{5} \cdot \frac{7}{8} = \frac{7 \cdot 7}{5 \cdot 1} = \frac{49}{5} = 9\frac{4}{5} = 9,8$ 2. $2\frac{5}{14} \cdot \frac{7}{9} = \frac{33}{14} \cdot \frac{7}{9} = \frac{11 \cdot 1}{2 \cdot 3} = \frac{11}{6} = 1\frac{5}{6}$ 3. $9\frac{4}{5} - 1\frac{5}{6} = 9\frac{24}{30} - 1\frac{25}{30} = 8\frac{54}{30} - 1\frac{25}{30} = 7\frac{29}{30}$ **Ответ: $7\frac{29}{30}$** в) $17,5 - 27 \cdot (\frac{5}{12} - \frac{3}{4})$ 1. $\frac{5}{12} - \frac{3}{4} = \frac{5}{12} - \frac{9}{12} = -\frac{4}{12} = -\frac{1}{3}$ 2. $27 \cdot (-\frac{1}{3}) = -9$ 3. $17,5 - (-9) = 17,5 + 9 = 26,5$ **Ответ: 26,5** г) $(-\frac{1}{3} - \frac{4}{7} - \frac{20}{21}) \cdot \frac{7}{13} + \frac{11}{25}$ 1. $-\frac{7}{21} - \frac{12}{21} - \frac{20}{21} = -\frac{39}{21} = -\frac{13}{7}$ 2. $-\frac{13}{7} \cdot \frac{7}{13} = -1$ 3. $-1 + \frac{11}{25} = -\frac{25}{25} + \frac{11}{25} = -\frac{14}{25} = -0,56$ **Ответ: -0,56** д) $(6\frac{1}{3} - 4,2) \cdot (-\frac{9}{16}) - 4,23$ 1. $6\frac{1}{3} - 4\frac{1}{5} = 6\frac{5}{15} - 4\frac{3}{15} = 2\frac{2}{15} = \frac{32}{15}$ 2. $\frac{32}{15} \cdot (-\frac{9}{16}) = -\frac{32 \cdot 9}{15 \cdot 16} = -\frac{2 \cdot 3}{5 \cdot 1} = -\frac{6}{5} = -1,2$ 3. $-1,2 - 4,23 = -5,43$ **Ответ: -5,43** е) $(-\frac{1}{4} - 0,75 - \frac{1}{5}) \cdot (-\frac{2}{3}) + 4,2$ 1. $-0,25 - 0,75 - 0,2 = -1 - 0,2 = -1,2 = -\frac{6}{5}$ 2. $-\frac{6}{5} \cdot (-\frac{2}{3}) = \frac{2 \cdot 2}{5 \cdot 1} = \frac{4}{5} = 0,8$ 3. $0,8 + 4,2 = 5$ **Ответ: 5**