1389. Найдите значение выражения: a) (1/14 - 1/7) : (-3) - 6/13 : (-6 1/13) б) (7 - 8/5) * 2/9 - 15 : (1/8 - 1/4) в) (204.12 : 10.5 - 3.2 - 1.2) * 6 1/2 + 7 : 2 1/3

Математика, 6 класс

Пошаговое решение:

• а)
  1. \[ \frac{1}{14} - \frac{1}{7} = \frac{1}{14} - \frac{2}{14} = -\frac{1}{14} \]
  2. \[ -\frac{1}{14} : (-3) = \frac{1}{14} \cdot \frac{1}{3} = \frac{1}{42} \]
  3. \[ -6\frac{1}{13} = -\frac{6  13 + 1}{13} = -\frac{78+1}{13} = -\frac{79}{13} \]
  4. \[ -\frac{79}{13} : \left(-\frac{79}{13}\right) = 1 \]
  5. \[ \frac{1}{42} - 1 = \frac{1}{42} - \frac{42}{42} = -\frac{41}{42} \]
• б)
  1. \[ 7 - \frac{8}{5} = \frac{35}{5} - \frac{8}{5} = \frac{27}{5} \]
  2. \[ \frac{27}{5} \cdot \frac{2}{9} = \frac{3 \cdot 9}{5} \cdot \frac{2}{9} = \frac{3 \cdot 2}{5} = \frac{6}{5} \]
  3. \[ \frac{1}{8} - \frac{1}{4} = \frac{1}{8} - \frac{2}{8} = -\frac{1}{8} \]
  4. \[ 15 : \left(-\frac{1}{8}\right) = 15 \cdot (-8) = -120 \]
  5. \[ \frac{6}{5} - (-120) = \frac{6}{5} + 120 = 1.2 + 120 = 121.2 \]
• в)
  1. \[ 204.12 : 10.5 \approx 19.44 \]
  2. \[ 19.44 - 3.2 - 1.2 = 15.04 \]
  3. \[ 6\frac{1}{2} = 6.5 \]
  4. \[ 15.04 \cdot 6.5 = 97.76 \]
  5. \[ 7 : 2\frac{1}{3} = 7 : \frac{7}{3} = 7 \cdot \frac{3}{7} = 3 \]
  6. \[ 97.76 + 3 = 100.76 \]

Ответ: а) -41/42, б) 121.2, в) 100.76