4.333 Найдите частное: a) \frac{6}{11} : (-1\frac{4}{11}); б) -1\frac{2}{9} : 3\frac{2}{3}; в) - 1\frac{1}{6} : (-\frac{1}{2}); г) -0,18 : (-2\frac{2}{5}); д) 0,1: (-\frac{1}{23}); e) \frac{3}{7} : 2,4.

Ответ:

a) -6/15; б) 3/10; в) 7/3; г) 5/66; д) -23/10; e) 5/28.

Решение:

• a) \(\frac{6}{11} : (-1\frac{4}{11}) = \frac{6}{11} : (-\frac{15}{11}) = \frac{6}{11} \cdot (-\frac{11}{15}) = -\frac{6}{15} = -\frac{2}{5}\)
• б) \(-1\frac{2}{9} : 3\frac{2}{3} = -\frac{11}{9} : \frac{11}{3} = -\frac{11}{9} \cdot \frac{3}{11} = -\frac{3}{9} = -\frac{1}{3}\)
• в) \(- 1\frac{1}{6} : (-\frac{1}{2}) = -\frac{7}{6} : (-\frac{1}{2}) = -\frac{7}{6} \cdot (-2) = \frac{7}{3}\)
• г) \(-0,18 : (-2\frac{2}{5}) = -\frac{18}{100} : (-\frac{12}{5}) = -\frac{18}{100} \cdot (-\frac{5}{12}) = \frac{90}{1200} = \frac{3}{40}\)
• д) \(0,1: (-\frac{1}{23}) = \frac{1}{10} : (-\frac{1}{23}) = \frac{1}{10} \cdot (-23) = -\frac{23}{10}\)
• е) \(\frac{3}{7} : 2,4 = \frac{3}{7} : \frac{24}{10} = \frac{3}{7} \cdot \frac{10}{24} = \frac{30}{168} = \frac{5}{28}\)

Ответ:

a) -6/15; б) 3/10; в) 7/3; г) 5/66; д) -23/10; e) 5/28.