Question

Find five rational numbers between $\frac{2}{3}$ and $\frac{3}{5}$

Answer 1

The $LCM$ of the denominators of the given rational numbers $\frac{2}{3}$ and $\frac{3}{5}$ is $LCM(3,5)=15$.

Therefore, with denominator $15$, the rational numbers becomes $\frac{10}{15}$ and $\frac{9}{15}$

The difference between the numerators $9$ and $10$ is very less, so we multiply both the numerators and denominators of the rational numbers $\frac{10}{15}$ and $\frac{9}{15}$ by $10$ to obtain the five rational numbers between them.

Now, the rational numbers becomes $\frac{100}{150}$ and $\frac{90}{150}$

Hence, the $5$ rational numbers between $\frac{90}{150}$ and $\frac{100}{150}$ are as follows:

$\frac{91}{150},\frac{93}{150},\frac{94}{150},\frac{97}{150},\frac{99}{150}$