Question

Arrange the following in descending order:

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

Answer 1

Step$1$: Find LCM of denominators of all the given fractions:

$\therefore$ LCM $\left(9,3,21\right)=63$

Step 2: Multiply the numerator and denominator of each fraction by a suitable number so that the denominator in each case becomes equal to LCM obtained in Step $1$:

$\therefore$ $\frac{2}{9}=\frac{2\times 7}{9\times 7}=\frac{14}{63}$

$\frac{2}{3}=\frac{2\times 21}{3\times 21}=\frac{42}{63}$

$\frac{8}{21}=\frac{8\times 3}{21\times 3}=\frac{24}{63}$

Step 3: Step $2$ would convert all fractions to like fractions and therefore the fraction with the greater numerator is greater:

$\because$ $42>24>14$

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

Therefore, the ascending order of fractions is: $\frac{2}{3},\frac{8}{21},\frac{2}{9}$