How to write fractions in descending order if the numerators are the same?

Solution:

Given a number of fractions whose numerators are different how to compare them and write them in descending order. It is obvious that their denominators are different and not the same. Otherwise, all the fractions would be the same or equal.

In such a situation, we find the LCM of the denominators of the fractions and then write the equivalent fractions of given fractions so that they all have same denominator equal to the LCM just now found. Now comparing the numerators makes it possible to arrange given fractions in descending order.

Example:

$\frac{2}{5}$,$ \frac{2}{9}$, $\frac{2}{6}$, $\frac{2}{8}$

All the numerators of given fractions are same 2

The LCM of 5, 6, 8 and 9 is 360

The fractions become

$\frac{2\times72}{5\times72}$, $\frac{2\times40}{9\times40}$, $\frac{2\times60}{6\times60}$, $\frac{2\times45}{8\times45}$

$\frac{144}{360}$, $\frac{80}{360}$, $\frac{120}{360}$, $\frac{90}{360}$

So arranging the numerators in descending order.

144 > 120 > 90 > 80

$\frac{2}{5}$, $\frac{2}{9}$, $\frac{2}{6}$, $\frac{2}{8}$ in descending order

Hence, 

$\frac{2}{5}$> $\frac{2}{6}$>$\frac{2}{8}$>$\frac{2}{9}$