447. Найди значение выражения, используя переход к натуральным числам: a) \(\frac{1-\frac{4}{7}}{1+\frac{4}{7}}\) б) \(\frac{3+\frac{1}{4}}{3-\frac{1}{4}}\) в) \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{\frac{1}{3}-\frac{1}{6}-\frac{1}{12}}\) г) \(\frac{\frac{2}{5}-\frac{3}{10}+\frac{11}{15}}{\frac{1}{2}+ \frac{2}{3}-\frac{1}{6}}\) д) \(\frac{\frac{1}{5}\cdot \frac{1}{9}\cdot \frac{1}{11}}{\frac{2}{5}\cdot \frac{2}{9}\cdot \frac{2}{11}}\) e) \(\frac{\frac{2}{3}\cdot \frac{5}{7}\cdot \frac{3}{20}}{\frac{1}{6}\cdot \frac{1}{7}\cdot \frac{13}{20}}\) ж) \(\frac{1\frac{2}{5}\cdot 2\frac{1}{7}}{1\frac{3}{7}\cdot 2\frac{4}{5}}\) з) \(\frac{2\frac{1}{2}\cdot \frac{1}{2}\cdot 2\frac{1}{4}}{1\frac{1}{2}\cdot \frac{1}{3}\cdot 1\frac{1}{4}}\)

Решение: a) \(\frac{1-\frac{4}{7}}{1+\frac{4}{7}} = \frac{\frac{7}{7}-\frac{4}{7}}{\frac{7}{7}+\frac{4}{7}} = \frac{\frac{3}{7}}{\frac{11}{7}} = \frac{3}{7} \cdot \frac{7}{11} = \frac{3}{11}\) б) \(\frac{3+\frac{1}{4}}{3-\frac{1}{4}} = \frac{\frac{12}{4}+\frac{1}{4}}{\frac{12}{4}-\frac{1}{4}} = \frac{\frac{13}{4}}{\frac{11}{4}} = \frac{13}{4} \cdot \frac{4}{11} = \frac{13}{11}\) в) \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{\frac{1}{3}-\frac{1}{6}-\frac{1}{12}} = \frac{\frac{6}{12}+\frac{4}{12}+\frac{3}{12}}{\frac{4}{12}-\frac{2}{12}-\frac{1}{12}} = \frac{\frac{13}{12}}{\frac{1}{12}} = \frac{13}{12} \cdot \frac{12}{1} = 13\) г) \(\frac{\frac{2}{5}-\frac{3}{10}+\frac{11}{15}}{\frac{1}{2}+ \frac{2}{3}-\frac{1}{6}} = \frac{\frac{12}{30}-\frac{9}{30}+\frac{22}{30}}{\frac{3}{6}+\frac{4}{6}-\frac{1}{6}} = \frac{\frac{25}{30}}{\frac{6}{6}} = \frac{25}{30} \cdot \frac{1}{1} = \frac{5}{6}\) д) \(\frac{\frac{1}{5}\cdot \frac{1}{9}\cdot \frac{1}{11}}{\frac{2}{5}\cdot \frac{2}{9}\cdot \frac{2}{11}} = \frac{1}{5\cdot 9\cdot 11} \cdot \frac{5\cdot 9\cdot 11}{2\cdot 2\cdot 2} = \frac{1}{8} \) e) \(\frac{\frac{2}{3}\cdot \frac{5}{7}\cdot \frac{3}{20}}{\frac{1}{6}\cdot \frac{1}{7}\cdot \frac{13}{20}} = \frac{2\cdot 5 \cdot 3}{3\cdot 7 \cdot 20} \cdot \frac{6\cdot 7 \cdot 20}{1 \cdot 1 \cdot 13} = \frac{2\cdot 5 \cdot 3 \cdot 6}{3 \cdot 13} = \frac{60}{39} = \frac{20}{13}\) ж) \(\frac{1\frac{2}{5}\cdot 2\frac{1}{7}}{1\frac{3}{7}\cdot 2\frac{4}{5}} = \frac{\frac{7}{5} \cdot \frac{15}{7}}{\frac{10}{7} \cdot \frac{14}{5}} = \frac{7 \cdot 15}{5 \cdot 7} \cdot \frac{7 \cdot 5}{10 \cdot 14} = \frac{105}{35} \cdot \frac{35}{140} = 3 \cdot \frac{1}{4} = \frac{3}{4}\) з) \(\frac{2\frac{1}{2}\cdot \frac{1}{2}\cdot 2\frac{1}{4}}{1\frac{1}{2}\cdot \frac{1}{3}\cdot 1\frac{1}{4}} = \frac{\frac{5}{2} \cdot \frac{1}{2} \cdot \frac{9}{4}}{\frac{3}{2} \cdot \frac{1}{3} \cdot \frac{5}{4}} = \frac{5 \cdot 1 \cdot 9}{2 \cdot 2 \cdot 4} \cdot \frac{2 \cdot 3 \cdot 4}{3 \cdot 1 \cdot 5} = \frac{45}{16} \cdot \frac{24}{15} = \frac{45}{16} \cdot \frac{8 \cdot 3}{5 \cdot 3} = \frac{9}{2} = 4\frac{1}{2}\)