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

P Pankaj Sanodiya

(i)

$\frac{2}{9}=\frac{2}{3\times3}\times\frac{7}{7}=\frac{14}{3\times3\times7}$

$\frac{2}{3}=\frac{2}{3}\times\frac{7}{7}\times\frac{3}{3}=\frac{42}{3\times3\times7}$

$\frac{8}{21}=\frac{8}{3\times7}\times\frac{3}{3}=\frac{24}{3\times3\times7}$

As 14 < 24 < 42

$\frac{2}{3}>\frac{8}{21}>\frac{2}{9}$

(ii)

$\frac{1}{5}=\frac{1}{5}\times\frac{14}{14}=\frac{14}{70}$

$\frac{3}{7}=\frac{3}{7}\times\frac{10}{10}=\frac{30}{70}$

$\frac{7}{10}=\frac{7}{10}\times\frac{7}{7}=\frac{49}{70}$

As 14 < 30 < 49

$\frac{7}{10}>\frac{3}{7}>\frac{1}{5}$

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