Question

Arrange the following in descending order :
$\frac{2}{9},\frac{2}{3},\frac{8}{21}$

Answer 1

Given fractions $\frac{2}{9},\frac{2}{3},\frac{8}{21}$

To compare any fractions, the denominators are must be same, so first let us make the denominators equal.

L.C. M of $9,3$ and $21$ is $63.$
$\Rightarrow \frac{2\times 7}{9\times 7}=\frac{14}{63}$

Similar way,
$\frac{2\times 21}{3\times 21}=\frac{42}{63}$
and $\frac{8\times 3}{21\times 3}=\frac{24}{63}$

Now, we can compare their numerators as $42>24>14$
Dividing $63$ by each number
$\frac{42}{63}>\frac{24}{63}>\frac{14}{63}$

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