Question

Find five rational numbers between:
$\frac{2}{3}$ and $\frac{4}{5}$

Answer 1

Given:$\frac{2}{3}$ and $\frac{4}{5}$

We know that there exists infinite numbers of rational numbers between two rational numbers. But to find any finite amount of ration numbers, we follow the given process.

LCM of $3$ and $5$ is $15$.

$\therefore \frac{2}{3}\times \frac{5}{5}=\frac{10}{15}$ and $\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}$

But we can only find one ration number between them and that is $\frac{11}{15}$. Therefore, we multiply numerator and denominator of both the rational numbers by a fixed numbers, lets say $4$, in this case.

$\therefore \frac{10}{15}\times \frac{4}{4}=\frac{40}{60}$ and $\frac{12}{15}\times \frac{4}{4}=\frac{48}{60}$

Hence, five rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ are $\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60},\frac{45}{60}$.