Question

Use LCM method to find three rational numbers that lie between $\frac{2}{5}$ and $\frac{3}{10}$.

Answer 1

The two given fractions are $\frac{2}{5}$ and $\frac{3}{10}$. The LCM of their denominators is $10.$ So, we multiply both the numerator and denominator of $\frac{2}{5}$ with 2 so as to make both the fractions on the same base.

Hence, the two fractions become $\frac{4}{10}$ and $\frac{3}{10}$. To find three numbers between them, we need to take $n=3+1=4$ and multiply $\frac{n}{n}$ with the fractions.

So, we get two fractions as $\frac{12}{40}$ and $\frac{16}{40}$.

Hence, the three fractions between them are $\frac{13}{40},\frac{14}{40},$ and $\frac{15}{40}$.