Question:
Evaluate:
(i) $\frac{-3}{5} \times \frac{10}{7}$
(ii) $\left(\frac{-5}{8}\right)^{-1}$
(iii) $(-6)^{-1}$
Solution:
(i) $\frac{-3}{5} \times \frac{10}{7}$
$=\frac{-3 \times 10}{5 \times 7}$
$=\frac{-30}{35}$
$=\frac{-6 \times 5}{7 \times 5}$
$=\frac{-6}{7}$
(ii) $\left(\frac{-5}{8}\right)^{-1}$
$=\frac{1}{\left(\frac{-5}{8}\right)}$
$=1 \times \frac{8}{-5}$
$=\frac{8}{-5}$
$=\frac{8 \times-1}{-5 \times-1}$
$=\frac{-8}{5}$
(iii) $(-6)^{-1}$
$=\frac{1}{-6}$
$=\frac{1 \times-1}{-6 \times-1}$
$=\frac{-1}{6}$