Решение:
а) $\frac{36 * (-112)}{126 * (-63)} = \frac{\overset{4}{\cancel{36}} * \overset{56}{\cancel{(-112)}}}{\underset{63}{\cancel{126}} * \underset{7}{\cancel{(-63)}}} = \frac{4 * \overset{8}{\cancel{(56)}}}{63 * \underset{1}{\cancel{7}}} = \frac{4 * 8}{63 * 1} = \frac{32}{63};$
б) $\frac{184 * (-49)}{84 * (-69)} = \frac{\overset{8}{\cancel{184}} * \overset{7}{\cancel{(-49)}}}{\underset{12}{\cancel{84}} * \underset{3}{\cancel{(-69)}}} = \frac{\overset{2}{\cancel{8}} * 7}{\underset{3}{\cancel{12}} * 3} = \frac{2 * 7}{3 * 3} = \frac{14}{9} = 1\frac{5}{9};$
в) $\frac{(-315) * 57}{114 * (-108)} = \frac{\overset{35}{\cancel{(-315)}} * \overset{1}{\cancel{57}}}{\underset{2}{\cancel{114}} * \underset{12}{\cancel{(-108)}}} = \frac{35 * 1}{2 * 12} = \frac{35}{24} = 1\frac{11}{24};$
г) $\frac{(-105) * 84}{196 * 125} = \frac{\overset{-21}{\cancel{(-105)}} * \overset{3}{\cancel{84}}}{ \underset{7}{\cancel{196}} * \underset{25}{\cancel{125}}} = \frac{\overset{-3}{\cancel{(-21)}} * 3}{\underset{1}{\cancel{7}} * 25} = -\frac{3 * 3}{1 * 25} = -\frac{9}{25};$
д) $\frac{(-111) * (-9)}{78 * 74} = \frac{\overset{3}{\cancel{(-111)}} * \overset{3}{\cancel{(-9)}}}{\underset{26}{\cancel{78}} * \underset{2}{\cancel{74}}} = \frac{3 * 3}{26 * 2} = \frac{9}{52};$
е) $\frac{(-888) * 55}{77 * 999} = \frac{\overset{8}{\cancel{(-888)}} * \overset{5}{\cancel{55}}}{\underset{7}{\cancel{77}} * \underset{9}{\cancel{999}}} = \frac{8 * 5}{7 * 9} = \frac{40}{63}.$
Ответ:
а) $\frac{32}{63};$
б) $1\frac{5}{9};$
в) $1\frac{11}{24};$
г) $-\frac{9}{25};$
д) $\frac{9}{52};$
е) $\frac{40}{63}.$