question_answer 20)

Which is greater: (i) \[\frac{2}{7}\]of \[\frac{3}{4}\]or \[\frac{3}{5}\]of \[\frac{5}{8}\]         (ii) \[\frac{1}{2}\]of \[\frac{6}{7}\]or \[\frac{2}{3}\]of \[\frac{3}{7}\]

Answer:

                (i) \[\frac{2}{7}\]of \[\frac{3}{4}=\frac{2}{7}\times \frac{3}{4}=\frac{2\times 3}{7\times 4}=\frac{6}{28}=\frac{6\div 2}{28\div 2}=\frac{3}{14}\] \[\frac{3}{5}\]of \[\frac{5}{8}=\frac{3}{5}\times \frac{5}{8}=\frac{3\times 5}{5\times 8}=\frac{15}{40}\]\[=\frac{15\div 5}{40\div 5}\]\[=\frac{3}{8}\] L.C.M. (14, 8) = 56 \[\frac{3}{14}=\frac{3\times 4}{14\times 4}=\frac{12}{56}\] \[\frac{3}{8}=\frac{3\times 7}{8\times 7}=\frac{21}{56}\] \[\because \]     \[21>12\] \[\therefore \]  \[\frac{21}{56}>\frac{12}{56}\] \[\therefore \]  \[\frac{3}{8}>\frac{3}{14}\] \[\therefore \]  \[\frac{3}{5}\]of \[\frac{5}{8}>\frac{2}{7}\]of \[\frac{3}{4}\] (ii)           \[\frac{1}{2}\]of \[\frac{6}{7}=\frac{1}{2}\times \frac{6}{7}=\frac{1\times 6}{2\times 7}=\frac{6}{14}=\frac{6\div 2}{14\div 2}=\frac{3}{7}\] \[\frac{2}{3}\]of \[\frac{3}{7}=\frac{2}{3}\times \frac{3}{7}=\frac{2\times 3}{3\times 7}=\frac{6}{21}=\]\[\frac{6\div 3}{21\div 3}\]\[=\frac{2}{7}\] \[\because \]     \[3>2\] \[\therefore \]  \[\frac{3}{7}>\frac{2}{7}\] \[\therefore \]  \[\frac{1}{2}\]of \[\frac{6}{7}>\frac{2}{3}\]of \[\frac{3}{7}\]