Question

Choose a rational number between $\frac{1}{5}$ and $\frac{1}{3}$.

• A. $0$
• B. $\frac{4}{15}$
• C. $\frac{15}{4}$
• D. $\frac{5}{3}$

Answer 1

The correct option is B $\frac{4}{15}$

$\text{Clearly,}\frac{1}{5},\frac{1}{3}>0and\frac{1}{5},\frac{1}{3}<1$
$\text{Hence, 0 does not lie between}\frac{1}{5}and\frac{1}{3}.$

$\frac{5}{3},\frac{15}{4}>1$
Hence,
$\frac{5}{3}\text{and}\frac{15}{4}\text{does not lie between}\frac{1}{5}and\frac{1}{3}$.

$\text{To find the rational number between}$
$\frac{1}{5}and\frac{1}{3}\text{, we need to alter the fractions}$
$\text{to get a common denomiantor.}$

$\frac{1}{5}=\frac{1\times 3}{5\times 3}=\frac{3}{15}$
$\frac{1}{3}=\frac{1\times 5}{3\times 5}=\frac{5}{15}$

$\frac{4}{15}\text{lies between}\frac{3}{15}\text{and}\frac{5}{15}$
$\text{So, it lies between}\frac{1}{5}and\frac{1}{3}.$