Question

Fill in the blanks by the correct symbol out of >, =, or <:
(i) $\frac{-6}{7}.....\frac{7}{13}$
(ii) $\frac{-3}{5}.....\frac{-5}{6}$
(iii) $\frac{-2}{3}.....\frac{5}{-8}$
(iv) $0.....\frac{-2}{5}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Because}\mathrm{every}\mathrm{positive}\mathrm{number}\mathrm{is}\mathrm{greater}\mathrm{than}\mathrm{a}\mathrm{negative}\mathrm{number},\frac{-6}{7}<\frac{7}{13}. \\ \left(\mathrm{ii}\right)\mathrm{On}\mathrm{multiplying}\frac{-3}{5}\mathrm{by}\frac{6}{6},\mathrm{we}\mathrm{get}\frac{-18}{30}. \\ \mathrm{On}\mathrm{multiplying}\frac{-5}{6}\mathrm{by}\frac{5}{5},\mathrm{we}\mathrm{get}\frac{-25}{30}. \\ \mathrm{Because}-18>-25,\frac{-3}{5}>\frac{-5}{6}. \\ \left(\mathrm{iii}\right)\mathrm{On}\mathrm{multiplying}\frac{-2}{3}\mathrm{by}\frac{8}{8},\mathrm{we}\mathrm{get}\frac{-16}{24}. \\ \mathrm{On}\mathrm{multiplying}\frac{5}{-8}\mathrm{by}\frac{3}{3},\mathrm{we}\mathrm{get}\frac{15}{-24}=\frac{-15}{24}. \\ \mathrm{Because}-15>-16,\frac{-2}{3}<\frac{5}{-8}. \\ \left(\mathrm{iv}\right)\mathrm{Because}\mathrm{every}\mathrm{positive}\mathrm{number}\mathrm{is}\mathrm{greater}\mathrm{than}\mathrm{a}\mathrm{negative}\mathrm{number},0>\frac{-2}{5}. \end{gathered}$$