Решение:
а) $5\frac{1}{2} * (-\frac{1}{4}) < 0;$
$5\frac{1}{2} * (-\frac{1}{4}) = \frac{11}{2} * (-\frac{1}{4}) = -\frac{11 * 1}{2 * 4} = -\frac{11}{8} = -1\frac{3}{8};$
б) $\frac{-3}{7} * 2\frac{1}{3} < 0;$
$\frac{-3}{7} * 2\frac{1}{3} = -\frac{3}{7} * \frac{7}{3} = -1;$
в) $(-\frac{7}{9}) * \frac{-8}{5} > 0;$
$(-\frac{7}{9}) * \frac{-8}{5} = \frac{7 * 8}{9 * 5} = \frac{56}{45} = 1\frac{11}{45};$
г) $\frac{-8}{-9} * \frac{-3}{-7} * \frac{-7}{-8} > 0;$
$\frac{-8}{-9} * \frac{-3}{-7} * \frac{-7}{-8} = \frac{8 * 3 * 7}{9 * 7 * 8} = \frac{3}{9} = \frac{1}{3};$
д) $(-\frac{1}{2}) : (-7) : (-3) < 0;$
$(-\frac{1}{2}) : (-7) : (-3) = (-\frac{1}{2}) * (-\frac{1}{7}) : (-\frac{1}{3}) = -\frac{1 * 1 * 1}{2 * 7 * 3} = -\frac{1}{42};$
е) ${(-\frac{4}{5})}^2 > 0;$
${(-\frac{4}{5})}^2 = (-\frac{4}{5}) * (-\frac{4}{5}) = \frac{16}{25}.$
Ответ:
а) $5\frac{1}{2} * (-\frac{1}{4}) < 0;$
$-1\frac{3}{8};$
б) $\frac{-3}{7} * 2\frac{1}{3} < 0;$
$-1;$
в) $(-\frac{7}{9}) * \frac{-8}{5} > 0;$
$(-\frac{7}{9}) * \frac{-8}{5} = \frac{7 * 8}{9 * 5} = \frac{56}{45} = 1\frac{11}{45};$
г) $\frac{-8}{-9} * \frac{-3}{-7} * \frac{-7}{-8} > 0;$
$\frac{1}{3};$
д) $(-\frac{1}{2}) : (-7) : (-3) < 0;$
$-\frac{1}{42};$
е) ${(-\frac{4}{5})}^2 > 0;$
$\frac{16}{25}.$