Question

Find three rational numbers lying between $\frac{3}{5}$ and $\frac{7}{8}$

How many rational numbers can be determined between these two numbers?

Answer 1

Given: Two rational numbers are $\frac{3}{5}$ and $\frac{7}{8}$

LCM of the denominators (i.e. $5$ and $8$) of the given rational numbers $=40$

Multiplying $\frac{3}{5}$ by $\frac{8}{8}$ and $\frac{7}{8}$ by $\frac{5}{5}$ to make the denominator equal i.e equal to the LCM(40).

$\Rightarrow \frac{3}{5}\times \frac{8}{8}=\frac{24}{40}$

and $\frac{7}{8}\times \frac{5}{5}=\frac{35}{40}$

$\frac{24}{40}<\frac{25}{40}<\frac{26}{40}<\frac{27}{40}<\frac{35}{40}$

So, the three rational number between $\frac{3}{5}=\frac{24}{40}$and $\frac{7}{8}=\frac{35}{40}$ are:-

$\frac{25}{40},\frac{26}{40},\frac{27}{40}$

There are infinite rational numbers between any two rational numbers.