Question

Arrange the fractions in ascending order

$\frac{2}{3},\frac{4}{5},\frac{6}{5},\frac{9}{8}$

Answer 1

To compare the given fractions, we have to make their denominators the same

So, the LCM of the denominators is $3\times 5\times 8=120$ [It is not always product of the numbers]

Converting all the fractions into a common base, $120,$ we get the fractions as:

$\frac{2}{3}\times \frac{40}{40}=\frac{80}{120}$

$\frac{4}{5}\times \frac{24}{24}=\frac{96}{120}$

$\frac{6}{5}\times \frac{24}{24}=\frac{144}{120}$

$\frac{9}{8}\times \frac{15}{15}=\frac{135}{120}$

Now, since the denominators are same, we can compare the numbers by comparing their numerators.

Arranging these in ascedning order we get, $\frac{80}{120},\frac{96}{120},\frac{135}{120},\frac{144}{120}$

Correspondingly arranging original fractions in ascending order, we get, $\frac{2}{3},\frac{4}{5},\frac{9}{8},\frac{6}{5}$