Решение:
а) $\frac{34}{35} : \frac{51}{55} = \frac{\overset{2}{\cancel{34}}}{\underset{7}{\cancel{35}}} * \frac{\overset{11}{\cancel{55}}}{\underset{3}{\cancel{51}}} = \frac{2 * 11}{7 * 3} = \frac{22}{21} = 1\frac{1}{21}$;
б) $\frac{\overset{1}{\cancel{37}}}{\underset{2}{\cancel{38}}} * \frac{\overset{3}{\cancel{57}}}{\underset{4}{\cancel{148}}} = \frac{1 * 3}{2 * 4} = \frac{3}{8}$;
в) $\frac{54}{125} * 35 = \frac{54}{\underset{25}{\cancel{125}}} * \frac{\overset{7}{\cancel{35}}}{1} = \frac{54 * 7}{25 * 1} = \frac{378}{25} = 15\frac{3}{25};$
г) $\frac{115}{116} : 62 = \frac{115}{116} * \frac{1}{62} = \frac{115 * 1}{116 * 62} = \frac{115}{7192}$;
д) $\frac{\overset{27}{\cancel{351}}}{\underset{5}{\cancel{625}}} * \frac{\overset{2}{\cancel{250}}}{\underset{14}{\cancel{182}}} = \frac{27}{5} * \frac{\overset{1}{\cancel{2}}}{\underset{7}{\cancel{14}}} = \frac{27 * 1}{5 * 7} = \frac{27}{35}$;
е) $99 : \frac{143}{120} = \frac{\overset{9}{\cancel{99}}}{1} * \frac{120}{\underset{13}{\cancel{143}}} = \frac{9 * 120}{1 * 13} = \frac{1080}{13} = 83\frac{1}{13}.$
Ответ:
а) $1\frac{1}{21}$;
б) $\frac{3}{8}$;
в) $15\frac{3}{25};$
г) $\frac{115}{7192}$;
д) $\frac{27}{35}$;
е) $83\frac{1}{13}.$