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

Consider $\frac{3}{5}$ and $\frac{7}{8}$

LCM of 5 and 8 = 40

So, making the denominators of both $\frac{3}{5}$ and $\frac{7}{8}$ equal to 40:

$\frac{3}{5}\times \frac{8}{8}=\frac{24}{40}$ and $\frac{7}{8}\times \frac{5}{5}=\frac{35}{40}$

Thus, $\frac{24}{40},\frac{25}{40},\frac{26}{40}$ are three rational numbers between the given numbers.

Also, there are infinite number of rational numbers between any two rational numbers.