6. Выполните действие: a) -4,2-(-7,5); 6) 3,8-(-1,15); в) -0,3-(-0,45) г) 7-(-0.4); д) -2(-1); e) 3,6-2,7:(-8,1) ж) -6,3: (-1,8)-3; з) -(-): e) 1:(-)-2

Решение:

a) \[ -4.2 - (-7.5) = -4.2 + 7.5 = 3.3 \]

б) \[ 3.8 - (-1.15) = 3.8 + 1.15 = 4.95 \]

в) \[ -0.3 - (-0.45) = -0.3 + 0.45 = 0.15 \]

г) \\(7 \frac{1}{3}) \cdot (-0.4) = \frac{22}{3} \cdot (-0.4) = -\frac{22}{3} \cdot \frac{4}{10} = -\frac{88}{30} = -\frac{44}{15} = -2 \frac{14}{15} \]

д) \[-2 \frac{6}{7}) : (-1 \frac{4}{14}) = -\frac{20}{7} : (-\frac{18}{14}) = -\frac{20}{7} : (-\frac{9}{7}) = \frac{20}{7} \cdot \frac{7}{9} = \frac{20}{9} = 2 \frac{2}{9}\]

е) \[3.6 - 2.7 : (-8.1) = 3.6 - (-\frac{1}{3}) = 3.6 + \frac{1}{3} = 3.6 + 0.(3) = 3.9(3)\]

ж) \[ -6.3 : (-1.8) \cdot 3 = 3.5 \cdot 3 = 10.5 \]

з) \[-\frac{2}{5} \cdot (-\frac{5}{8}) : \frac{3}{4} = \frac{2}{5} \cdot \frac{5}{8} \cdot \frac{4}{3} = \frac{2 \cdot 5 \cdot 4}{5 \cdot 8 \cdot 3} = \frac{2 \cdot 1 \cdot 1}{1 \cdot 2 \cdot 3} = \frac{2}{6} = \frac{1}{3}\]

и) \[1 \frac{2}{3} : (-\frac{5}{6}) \cdot 2 \frac{2}{5} = \frac{5}{3} \cdot (-\frac{6}{5}) \cdot \frac{12}{5} = -\frac{5 \cdot 6 \cdot 12}{3 \cdot 5 \cdot 5} = -\frac{1 \cdot 2 \cdot 12}{1 \cdot 1 \cdot 5} = -\frac{24}{5} = -4 \frac{4}{5}\]