Question

Select the rational numbers which lie between $\frac{2}{5}$ and $\frac{3}{10}$. Use the LCM method.

• A. $\frac{13}{10},\frac{14}{10}$, and $\frac{15}{10}$.
• B. $\frac{13}{40},\frac{14}{40},$ and $\frac{15}{40}$.
• C. $\frac{13}{20},\frac{14}{20}$, and $\frac{15}{20}$.
• D. $\frac{13}{5},\frac{14}{5}$, and $\frac{15}{20}$.

Answer 1

The correct option is B

$\frac{13}{40},\frac{14}{40},$ and $\frac{15}{40}$.

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 $\frac{15}{40}$.