question_answer 2)

Arrange the following in descending order: (i) \[\frac{2}{9},\frac{2}{3},\frac{8}{21}\]                               (ii) \[\frac{1}{5},\frac{3}{7},\frac{7}{10}.\]                

Answer:

                (i) Converting the given fractions into like fractions, we have                 \[\frac{2}{9}=\frac{2\times 7}{9\times 7}=\frac{14}{63}\]                 \[\frac{2}{3}=\frac{2\times 21}{3\times 21}=\frac{42}{63}\]                 \[\frac{8}{21}=\frac{8\times 3}{21\times 3}=\frac{24}{63}\] \[\because \]     \[42>24>14\] \[\therefore \]  \[\frac{42}{63}>\frac{24}{63}>\frac{14}{63}\] \[\therefore \]  \[\frac{2}{3}>\frac{8}{21}>\frac{2}{9}\] (ii) Converting the given fractions into like fractions, we have \[\frac{1}{5}=\frac{1\times 14}{5\times 14}=\frac{14}{70}\] \[\frac{3}{7}=\frac{3\times 10}{7\times 10}=\frac{30}{70}\] \[\frac{7}{10}=\frac{7\times 7}{10\times 7}=\frac{49}{70}\] \[\because \]     \[49>30>14\] \[\therefore \]  \[\frac{49}{70}>\frac{30}{70}>\frac{14}{70}\] \[\therefore \]  \[\frac{7}{10}>\frac{3}{7}>\frac{1}{5}\]