302 Выполни действия: а) 3/5 - 5/7; б) -2 1/7 * (-1 3/25); в) -3 3/5 : (-1 1/12) * (-6.8) * 9/8 : (-1 1/7); г) -5.4 * (-1 2/9) : 3.75 * (-4 1/5)

Решение:

1. а)

   \[ \frac{3}{5} - \frac{5}{7} = \frac{3 \times 7 - 5 \times 5}{35} = \frac{21 - 25}{35} = -\frac{4}{35} \]

2. б)

   \[ -2 \frac{1}{7} \times \left( -1 \frac{3}{25} \right) = -\frac{15}{7} \times \left( -\frac{28}{25} \right) = \frac{15 \times 28}{7 \times 25} = \frac{3 \times 5 \times 4 \times 7}{7 \times 5 \times 5} = \frac{12}{5} = 2 \frac{2}{5} \]

3. в)

   \[ -3 \frac{3}{5} : \left( -1 \frac{1}{12} \right) \times (-6.8) \times \frac{9}{8} : \left( -1 \frac{1}{7} \right) \]

   \[ = -\frac{18}{5} : \left( -\frac{13}{12} \right) \times \left( -\frac{68}{10} \right) \times \frac{9}{8} : \left( -\frac{8}{7} \right) \]

   \[ = -\frac{18}{5} \times \left( -\frac{12}{13} \right) \times \left( -\frac{34}{5} \right) \times \frac{9}{8} \times \left( -\frac{7}{8} \right) \]

   Произведение четырех отрицательных чисел будет положительным.

   \[ = \frac{18 \times 12 \times 34 \times 9 \times 7}{5 \times 13 \times 5 \times 8 \times 8} = \frac{2 \times 9 \times 12 \times 34 \times 9 \times 7}{5 \times 13 \times 5 \times 8 \times 8} = \frac{9 \times 3 \times 34 \times 9 \times 7}{5 \times 13 \times 5 \times 2 \times 8} = \frac{255066}{41600} \]

   Упростим:

   \[ \frac{18}{5} \times \frac{12}{13} \times \frac{34}{5} \times \frac{9}{8} \times \frac{7}{8} = \frac{18}{5} \times \frac{12}{13} \times \frac{17}{5} \times \frac{9}{4} \times \frac{7}{8} \]

   \[ = \frac{9 \times 3 \times 17 \times 9 \times 7}{5 \times 13 \times 5 \times 2 \times 8} = \frac{34878}{2600} \]

   Необходимо пересчитать.

   \[ -\frac{18}{5} : \left( -\frac{13}{12} \right) = -\frac{18}{5} \times \frac{-12}{13} = \frac{216}{65} \]

   \[ \frac{216}{65} \times \frac{-34}{5} = -\frac{7344}{325} \]

   \[ -\frac{7344}{325} \times \frac{9}{8} = -\frac{918}{325} \]

   \[ -\frac{918}{325} : \left( -\frac{8}{7} \right) = -\frac{918}{325} \times \frac{-7}{8} = \frac{6426}{2600} = \frac{3213}{1300} = 2 \frac{613}{1300} \]

4. г)

   \[ -5.4 \times \left( -1 \frac{2}{9} \right) : 3.75 \times \left( -4 \frac{1}{5} \right) \]

   \[ = -\frac{54}{10} \times \left( -\frac{11}{9} \right) : \frac{375}{100} \times \left( -\frac{21}{5} \right) \]

   \[ = -\frac{27}{5} \times \left( -\frac{11}{9} \right) : \frac{15}{4} \times \left( -\frac{21}{5} \right) \]

   \[ = \frac{27 \times 11}{5 \times 9} \times \frac{4}{15} \times \left( -\frac{21}{5} \right) \]

   \[ = \frac{3 \times 11}{5} \times \frac{4}{15} \times \left( -\frac{21}{5} \right) = \frac{33}{5} \times \frac{4}{15} \times \left( -\frac{21}{5} \right) \]

   \[ = \frac{33 \times 4}{5 \times 15} \times \left( -\frac{21}{5} \right) = \frac{11 \times 4}{5 \times 5} \times \left( -\frac{21}{5} \right) = \frac{44}{25} \times \left( -\frac{21}{5} \right) \]

   \[ = -\frac{44 \times 21}{25 \times 5} = -\frac{924}{125} = -7 \frac{49}{125} \]

Ответ: а) -4/35; б) 2 2/5; в) 3213/1300; г) -7 49/125