Сократите дробь:
а) $\frac{-3 * 8 * (-6)}{18 * (-4)};$
б) $\frac{-7 * 16}{-14 * (-2) * (-10)};$
в) $\frac{-2 * (-3) * (-6)}{-3 * (-8) * (-10)};$
г) $\frac{-96 * (-125)}{-75 * (-128)};$
д) $\frac{56 * (-77)}{-121 * (-49)};$
е) $\frac{-128 * (-92)}{-256 * (-48)}.$
Решение:
а) $\frac{-3 * 8 * (-6)}{18 * (-4)} = \frac{18 * 8}{18 * (-4)} = \frac{\overset{1}{\cancel{18}} * \overset{2}{\cancel{8}}}{\underset{1}{\cancel{18}} * \underset{-1}{\cancel{(-4)}}} = \frac{1 * 2}{1 * (-1)} = -\frac{2}{1} = -2;$
б) $\frac{-7 * 16}{-14 * (-2) * (-10)} = \frac{\overset{1}{\cancel{-7}} * \overset{8}{\cancel{16}}}{\underset{2}{\cancel{-14}} * \underset{-1}{\cancel{(-2)}} * (-10)} = \frac{1 * \overset{1}{\cancel{2}} * \overset{2}{\cancel{4}}}{\underset{1}{\cancel{(2)}} * (-1) * \underset{-5}{\cancel{(-10)}}} = \frac{1 * 1 * 2}{1 * (-1) * (-5)} = \frac{2}{5};$
в) $\frac{-2 * (-3) * (-6)}{-3 * (-8) * (-10)} = \frac{\overset{1}{\cancel{-2}} * \overset{1}{\cancel{(-3)}} * \overset{3}{\cancel{(-6)}}}{\underset{1}{\cancel{-3}} * \underset{4}{\cancel{(-8)}} * \underset{5}{\cancel{(-10)}}} = \frac{1 * 1 * 3}{1 * 4 * 5} = \frac{3}{20};$
г) $\frac{-96 * (-125)}{-75 * (-128)} = \frac{\overset{3}{\cancel{-96}} * \overset{5}{\cancel{(-125)}}}{\underset{3}{\cancel{-75}} * \underset{4}{\cancel{(-128)}}} = \frac{\overset{1}{\cancel{3}} * 5}{4 * \underset{1}{\cancel{3}}} = \frac{1 * 5}{4 * 1} = \frac{5}{4} = 1\frac{1}{4};$
д) $\frac{56 * (-77)}{-121 * (-49)} = \frac{\overset{8}{\cancel{56}} * \overset{7}{\cancel{(-77)}}}{\underset{11}{\cancel{(-121)}} * \underset{-7}{\cancel{(-49)}}} = \frac{8 * \overset{1}{\cancel{7}}}{11 * \underset{-1}{\cancel{(-7)}}} = \frac{8 * 1}{11 * (-1)} = -\frac{8}{11};$
е) $\frac{-128 * (-92)}{-256 * (-48)} = \frac{\overset{1}{\cancel{-128}} * \overset{23}{\cancel{(-92)}}}{\underset{2}{\cancel{(-256)}} * \underset{12}{\cancel{(-48)}}} = \frac{1 * 23}{2 * 12} = \frac{23}{24}.$
Ответ:
а) $-2;$
б) $\frac{2}{5};$
в) $\frac{3}{20};$
г) $1\frac{1}{4};$
д) $-\frac{8}{11};$
е) $\frac{23}{24}.$
Пожауйста, оцените решение