question_answer 1)

Which is grater in each of the following: (i) \[\frac{2}{3},\frac{5}{2}\]                                        (ii) \[\frac{-5}{6},\frac{-4}{3}\]                    (iii) \[\frac{-3}{4},\frac{2}{-3}\]                           (iv) \[\frac{-1}{4},\frac{1}{4}\] (v) \[-3\frac{2}{7},-3\frac{4}{5}\].

Answer:

                (i) \[\frac{2}{3}=\frac{2\times 2}{3\times 2}=\frac{4}{6}\]                                              \[\left| \text{LCM(3,2) = 6} \right.\]                 \[\frac{5}{2}=\frac{5\times 3}{2\times 3}=\frac{15}{6}\]  \[\because \]    \[\frac{15}{6}>\frac{4}{6}\] \[\therefore \]  \[\frac{5}{2}>\frac{2}{3}\]                 (ii) \[\frac{-5}{6}=\frac{-5}{6}\]                 \[\frac{-4}{3}=\frac{-4\times 2}{3\times 2}=\frac{-8}{6}\]                                              \[\left| \text{LCM (6,3) = 6} \right.\] \[\because \]     \[\frac{-5}{6}>\frac{-8}{6}\] \[\therefore \]  \[-\frac{5}{6}>\frac{-4}{3}\]                 (iii) \[\frac{-3}{4}=\frac{-3\times 3}{4\times 3}=\frac{-9}{12}\]                 \[\frac{2}{-3}=\frac{2\times 4}{-3\times 4}=\frac{8}{-12}=\frac{-8}{12}\]                                \[\left| \text{LCM (4,3) =12} \right.\] \[\because \]     \[\frac{-8}{12}>\frac{-9}{12}\] \[\therefore \]  \[\frac{2}{-3}>\frac{-3}{4}\]                 (iv) \[\frac{1}{4}>-\frac{1}{4}\]                 (v) \[-3\frac{2}{7}=-\frac{23}{7}=\frac{-23\times 5}{7\times 5}=\frac{-115}{35}\]                \[\left| \text{LCM (7,5) = 35} \right.\] \[-3\frac{4}{5}=\frac{-19}{5}=\frac{-19\times 7}{5\times 7}=\frac{-133}{35}\] \[\because \]     \[\frac{-115}{35}>\frac{-133}{35}\] \[\therefore \]  \[-3\frac{2}{7}>-3\frac{4}{5}\].