Q.2 Arrange the following in descending order: (i)$$\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$$
(ii) $$\frac{1}{5} ,\frac{3}{7}, \frac{7}{10}$$
(i)$$\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$$
$$\frac{2}{9}=\frac{2×7}{9×7}=\frac{14}{63}$$ $$\frac{2}{3}=\frac{2×21}{3×21}=\frac{42}{63}$$ $$\frac{8}{21}=\frac{8×3}{21×3}=\frac{24}{63}$$ Hence $$\frac{42}{63} > \frac{24}{63} > \frac{14}{63}$$
$$\frac{2}{3} > \frac{8}{21} > \frac{2}{9}$$
(ii) $$\frac{1}{5} ,\frac{3}{7}, \frac{7}{10}$$
$$\frac{1}{5}=\frac{1×14}{5×14}=\frac{14}{70}$$ $$\frac{3}{7}=\frac{3×10}{7×10}=\frac{21}{70}$$ $$\frac{7}{10}=\frac{7×7}{10×7}=\frac{49}{70}$$ Hence $$\frac{49}{70} > \frac{21}{70} > \frac{14}{70}$$
$$\frac{7}{10} > \frac{3}{7} > \frac{1}{5}$$