Выполните действия: $6\frac{2}{25} + 7\frac{23}{25} - 4\frac{1}{40}$

№4. Выполните действия: а) $6\frac{2}{25} + 7\frac{23}{25} - 4\frac{1}{40} = (6+7) + (\frac{2}{25} + \frac{23}{25}) - 4\frac{1}{40} = 13 + \frac{25}{25} - 4\frac{1}{40} = 13 + 1 - 4\frac{1}{40} = 14 - 4\frac{1}{40} = 13\frac{40}{40} - 4\frac{1}{40} = (13-4) + (\frac{40}{40} - \frac{1}{40}) = 9 + \frac{39}{40} = 9\frac{39}{40}$ **Ответ: $9\frac{39}{40}$** б) $20\frac{1}{19} - 4\frac{12}{19} - 5\frac{17}{19} = \frac{20 \cdot 19 + 1}{19} - \frac{4 \cdot 19 + 12}{19} - \frac{5 \cdot 19 + 17}{19} = \frac{380 + 1}{19} - \frac{76 + 12}{19} - \frac{95 + 17}{19} = \frac{381}{19} - \frac{88}{19} - \frac{112}{19} = \frac{381 - 88 - 112}{19} = \frac{293 - 112}{19} = \frac{181}{19} = 9\frac{10}{19}$ **Ответ: $9\frac{10}{19}$** в) $(6\frac{5}{24} + 7\frac{19}{24}) - 6\frac{19}{23} - 5\frac{9}{23} = (6+7) + (\frac{5}{24} + \frac{19}{24}) - 6\frac{19}{23} - 5\frac{9}{23} = 13 + \frac{24}{24} - 6\frac{19}{23} - 5\frac{9}{23} = 13 + 1 - 6\frac{19}{23} - 5\frac{9}{23} = 14 - (6\frac{19}{23} + 5\frac{9}{23}) = 14 - ((6+5) + (\frac{19}{23} + \frac{9}{23})) = 14 - (11 + \frac{28}{23}) = 14 - (11 + 1\frac{5}{23}) = 14 - 12\frac{5}{23} = 13\frac{23}{23} - 12\frac{5}{23} = (13-12) + (\frac{23}{23} - \frac{5}{23}) = 1 + \frac{18}{23} = 1\frac{18}{23}$ **Ответ: $1\frac{18}{23}$** №5. Выполните действия: а) $10\frac{4}{15} + 9\frac{11}{15} - 8\frac{1}{30} = (10+9) + (\frac{4}{15} + \frac{11}{15}) - 8\frac{1}{30} = 19 + \frac{15}{15} - 8\frac{1}{30} = 19 + 1 - 8\frac{1}{30} = 20 - 8\frac{1}{30} = 19\frac{30}{30} - 8\frac{1}{30} = (19-8) + (\frac{30}{30} - \frac{1}{30}) = 11 + \frac{29}{30} = 11\frac{29}{30}$ **Ответ: $11\frac{29}{30}$** б) $19\frac{1}{17} - 8\frac{9}{17} - 3\frac{15}{17} = \frac{19 \cdot 17 + 1}{17} - \frac{8 \cdot 17 + 9}{17} - \frac{3 \cdot 17 + 15}{17} = \frac{323 + 1}{17} - \frac{136 + 9}{17} - \frac{51 + 15}{17} = \frac{324}{17} - \frac{145}{17} - \frac{66}{17} = \frac{324 - 145 - 66}{17} = \frac{179 - 66}{17} = \frac{113}{17} = 6\frac{11}{17}$ **Ответ: $6\frac{11}{17}$** в) $(6\frac{7}{12} + 8\frac{5}{12}) - 7\frac{16}{21} - 4\frac{6}{21} = (6+8) + (\frac{7}{12} + \frac{5}{12}) - 7\frac{16}{21} - 4\frac{6}{21} = 14 + \frac{12}{12} - 7\frac{16}{21} - 4\frac{6}{21} = 14 + 1 - 7\frac{16}{21} - 4\frac{6}{21} = 15 - (7\frac{16}{21} + 4\frac{6}{21}) = 15 - ((7+4) + (\frac{16}{21} + \frac{6}{21})) = 15 - (11 + \frac{22}{21}) = 15 - (11 + 1\frac{1}{21}) = 15 - 12\frac{1}{21} = 14\frac{21}{21} - 12\frac{1}{21} = (14-12) + (\frac{21}{21} - \frac{1}{21}) = 2 + \frac{20}{21} = 2\frac{20}{21}$ **Ответ: $2\frac{20}{21}$**