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

Решение:

а) $$7\frac{11}{12}:3\frac{1}{6} = \frac{7 \cdot 12 + 11}{12} : \frac{3 \cdot 6 + 1}{6} = \frac{84 + 11}{12} : \frac{18 + 1}{6} = \frac{95}{12} : \frac{19}{6} = \frac{95}{12} \cdot \frac{6}{19} = \frac{95 \cdot 6}{12 \cdot 19} = \frac{5 \cdot 1}{2 \cdot 1} = \frac{5}{2} = 2\frac{1}{2}$$

б) $$2\frac{3}{5}:\frac{4}{15} = \frac{2 \cdot 5 + 3}{5} : \frac{4}{15} = \frac{10 + 3}{5} : \frac{4}{15} = \frac{13}{5} : \frac{4}{15} = \frac{13}{5} \cdot \frac{15}{4} = \frac{13 \cdot 15}{5 \cdot 4} = \frac{13 \cdot 3}{1 \cdot 4} = \frac{39}{4} = 9\frac{3}{4}$$

в) $$\frac{3,4}{20,4} = \frac{3,4 \cdot 10}{20,4 \cdot 10} = \frac{34}{204} = \frac{17 \cdot 2}{17 \cdot 12} = \frac{1}{6}$$

г) $$\frac{1,71}{4\frac{1}{5}} = \frac{1,71}{\frac{4 \cdot 5 + 1}{5}} = \frac{1,71}{\frac{20 + 1}{5}} = \frac{1,71}{\frac{21}{5}} = 1,71 : \frac{21}{5} = 1,71 \cdot \frac{5}{21} = \frac{171}{100} \cdot \frac{5}{21} = \frac{57 \cdot 3}{20 \cdot 5} \cdot \frac{5}{7 \cdot 3} = \frac{57 \cdot 1}{20 \cdot 1} \cdot \frac{1}{7 \cdot 1} = \frac{57}{140}$$

Ответ: а) $$2\frac{1}{2}$$; б) $$9\frac{3}{4}$$; в) $$\frac{1}{6}$$; г) $$\frac{57}{140}$$