question_answer 8)

Fill in the boxes with the correct symbol out of >, < and = (i) \[\frac{-5}{7}\frac{2}{3}\]                        (ii) \[\frac{-4}{5}\frac{-5}{7}\]                     (iii) \[\frac{-7}{8}\frac{14}{-16}\]                      (iv) \[\frac{-8}{5}\frac{-7}{4}\] (v) \[\frac{1}{-3}\frac{-1}{4}\]                     (vi) \[\frac{5}{-11}\frac{-5}{11}\]                               (vii) \[0\frac{-7}{6}\]

Answer:

                (i) \[\frac{-5}{7}<\frac{2}{3}\] \[\left| \begin{align}   & \frac{\text{-5}}{\text{7}}\text{is a negative rational number whereas} \\  & \frac{\text{2}}{\text{3}}\text{is a positive ratinal number}\text{.} \\ \end{align} \right.\] (ii) \[\frac{-4}{5}\frac{-5}{7}\]     \[\left| \begin{align}   & \frac{-4}{5}=\frac{-4\times 7}{5\times 7}=\frac{-28}{35} \\  & \frac{-5}{7}=\frac{-5\times 5}{7\times 5}=\frac{-25}{35} \\ \end{align} \right.\]                 (iii) \[\frac{-7}{8}\frac{14}{-16}\] \[\left| \frac{-7}{8}=\frac{-7\times -2}{8\times -2} \right.=\frac{14}{-16}\]                 (iv) \[\frac{-8}{5}\frac{-7}{4}\] \[\left| \begin{align}   & \frac{-8}{5}=\frac{-8\times 4}{5\times 4}=\frac{-32}{20} \\  & \frac{-7}{4}=\frac{-7\times 5}{4\times 5}=\frac{-35}{20} \\ \end{align} \right.\]                 (v) \[\frac{1}{-3}\frac{-1}{4}\] \[\left| \begin{align}   & \frac{1}{-3}=\frac{1\times -4}{-3\times -4}=\frac{-4}{12} \\  & \frac{-1}{4}=\frac{-1\times 3}{4\times 3}=\frac{-3}{12} \\ \end{align} \right.\]                 (vi) \[\frac{5}{-11}\frac{-5}{11}.\]                 \[\left| \frac{5}{-11}=\frac{5\times -1}{-11\times -1}=\frac{-5}{11} \right.\]                 (vii) \[0\frac{-7}{6}.\]