Question

What are the five rational numbers between $\frac{3}{5}$and$\frac{4}{5}$?

Answer 1

Find rational numbers between two numbers:

A rational number is a number that can be expressed in $\frac{p}{q}$form. Where $p$and $q$are integers and $q\ne 0$.

To find five rational numbers between $\frac{3}{5}$and$\frac{4}{5}$, multiply by $6$ to both numerator and denominator.

We get,

$$\begin{gathered} \frac{3}{5}\times \frac{6}{6}=\frac{18}{30} \\ \frac{4}{5}\times \frac{6}{6}=\frac{24}{30} \end{gathered}$$

All the fractions between $\frac{18}{30}$and $\frac{24}{30}$are required rational numbers which lie between two given numbers.

So, $\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30}$and $\frac{23}{30}$are required rational numbers.

Hence, the five rational numbers between $\frac{3}{5}$and $\frac{4}{5}$are $\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30}$and$\frac{23}{30}$.