Вариант 2 1. Найдите значение выражения: a) $$7\frac{11}{12}:3\frac{1}{6}$$; б) $$\frac{\frac{3}{5}}{\frac{4}{2 \frac{2}{15}}}$$; в) $$\frac{3,4}{20,4}$$; г) $$\frac{1,71}{4 \frac{1}{5}}$$

Это задание по математике, необходимо вычислить значение выражений.

a) $$7\frac{11}{12}:3\frac{1}{6} = \frac{7\times12 + 11}{12} : \frac{3\times6+1}{6} = \frac{95}{12}:\frac{19}{6} = \frac{95}{12} \cdot \frac{6}{19} = \frac{5\times19}{2\times6} \cdot \frac{6}{19} = \frac{5}{2} = 2,5$$

б) $$\frac{\frac{3}{5}}{\frac{4}{2 \frac{2}{15}}} = \frac{\frac{3}{5}}{\frac{4}{\frac{2\times15+2}{15}}} = \frac{\frac{3}{5}}{\frac{4}{\frac{32}{15}}} = \frac{\frac{3}{5}}{\frac{4 \times 15}{32}} = \frac{\frac{3}{5}}{\frac{60}{32}} = \frac{3}{5} : \frac{15}{8} = \frac{3}{5} \cdot \frac{8}{15} = \frac{1}{5} \cdot \frac{8}{5} = \frac{8}{25} = 0,32$$

в) $$\frac{3,4}{20,4} = \frac{34}{204} = \frac{17}{102} = \frac{1}{6} \approx 0,167$$

г) $$\frac{1,71}{4 \frac{1}{5}} = \frac{1,71}{\frac{4\times5+1}{5}} = \frac{1,71}{\frac{21}{5}} = 1,71 : \frac{21}{5} = \frac{171}{100} \cdot \frac{5}{21} = \frac{57}{20} \cdot \frac{1}{7} = \frac{19}{20} \cdot \frac{1}{7} = \frac{19}{140} \approx 0,136$$