333 Найдите частное: a) 6/11: (-1 4/11); б) -1 2/9 : 3 2/3; в) -1 1/6 : (-1/2); г) -0,18: (-2 2/5);

Найдем частное:

1. $$\frac{6}{11} : (-1\frac{4}{11}) = \frac{6}{11} : (-\frac{15}{11}) = \frac{6}{11} \cdot (-\frac{11}{15}) = \frac{6 \cdot (-11)}{11 \cdot 15} = \frac{6 \cdot (-1)}{1 \cdot 15} = \frac{-6}{15} = -\frac{2}{5} = -0,4$$
2. $$-1\frac{2}{9} : 3\frac{2}{3} = -\frac{11}{9} : \frac{11}{3} = -\frac{11}{9} \cdot \frac{3}{11} = \frac{-11 \cdot 3}{9 \cdot 11} = \frac{-1 \cdot 1}{3 \cdot 1} = -\frac{1}{3} = -0,(3)$$
3. $$-1\frac{1}{6} : (-\frac{1}{2}) = -\frac{7}{6} : (-\frac{1}{2}) = -\frac{7}{6} \cdot (-2) = \frac{-7 \cdot (-2)}{6} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3}$$
4. $$-0,18 : (-2\frac{2}{5}) = -0,18 : (-\frac{12}{5}) = -\frac{18}{100} : (-\frac{12}{5}) = -\frac{18}{100} \cdot (-\frac{5}{12}) = \frac{-18 \cdot (-5)}{100 \cdot 12} = \frac{3 \cdot 1}{20 \cdot 2} = \frac{3}{40} = 0,075$$

Ответ: a) -0,4; б) -1/3; в) 2 1/3; г) 0,075