Find any five rational numbers between $\frac{3}{5}$ and $\frac{5}{6}$

To do:

Find any five rational numbers between $\frac{3}{5}$ and $\frac{5}{6}$

Solution:

To solve this question, first we need to convert them into like fractions.

We take LCM of $\frac{3}{5}$ and $\frac{5}{6}$

LCM of denominators is 30.

Now we have change the fractions in such a way that denominators become 30

To convert into like fractions we will multiply numerator and denominator of  $\frac{3}{5}$ with 6.

$ \frac{3}{5} = \frac{3}{5}\times\frac{6}{6} = \frac{18}{30}$

We will multiply numerator and denominator of 5/6 with 5.

$\frac{5}{6} = \frac{5}{6}\times\frac{5}{5} = \frac{25}{30}$

Now our numbers are $\frac{18}{30}$ and $\frac{25}{30}$.

Now we find Rational Numbers between them that is

$\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$