question_answer 1)

Write the following rational numbers in ascending order: (i) \[\frac{-3}{5},\frac{-2}{5},\frac{-1}{5}\]                             (ii) \[\frac{-1}{3},\frac{-2}{9},\frac{-4}{3}\]                            (iii) \[\frac{-3}{7},\frac{-3}{2},\frac{-3}{4}\]                          

Answer:

                (i) The given rational numbers in ascending order are \[\frac{-3}{5},\frac{-2}{5},\frac{-1}{5}\]                 (ii) \[\frac{-1}{3}=\frac{-1\times 3}{3\times 3}=\frac{-3}{9}\]                        \[\left| \text{LCM (3,9,3)} \right.\text{ = 9}\]                 \[\frac{-2}{9}=\frac{-2}{9}\]                 \[\frac{-4}{3}=\frac{-4\times 3}{3\times 3}=\frac{-12}{9}\] \[\because \]     \[\frac{-12}{9}<\frac{-3}{9}<\frac{-2}{9}\] \[\therefore \]  \[\frac{-4}{3}<\frac{-1}{3}<\frac{-2}{9}\]                 (iii) \[\frac{-3}{7}=\frac{-3\times 4}{7\times 4}=\frac{-12}{28}\]                  \[\left| \text{LCM (7, 2, 4) = 28} \right.\]                 \[\frac{-3}{2}=\frac{-3\times 14}{2\times 14}=\frac{-42}{28}\]                 \[\frac{-3}{4}=\frac{-3\times 7}{4\times 7}=\frac{-21}{28}\] \[\because \]     \[-\frac{42}{28}<-\frac{21}{28}<-\frac{12}{28}\] \[\therefore \]  \[-\frac{3}{2}<-\frac{3}{4}<-\frac{3}{7}\].