Question

Arrange the following in ascending order.

$\frac{4}{7},\frac{5}{9},\frac{2}{5}$

Answer 1

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

$\therefore$ LCM $\left(7,9,5\right)$$=315$

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

$\therefore$ $\frac{4}{7}=\frac{4\times 45}{7\times 45}=\frac{180}{315}$

$\frac{5}{9}=\frac{5\times 35}{9\times 35}=\frac{175}{315}$

$\frac{2}{5}=\frac{2\times 63}{5\times 63}=\frac{126}{315}$

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

$\because$ $126<175<180$

$\therefore$ $\frac{2}{5}<\frac{5}{9}<\frac{4}{7}$

Therefore, the ascending order of fractions is: $\frac{2}{5},\frac{5}{9},\frac{4}{7}$