Question

A rational no. Between 1/7and2/7 is •1/14
•2/21
•5/14
•5/21

Answer 1

$\large{\underline{\boxed{\text{Question:}}}} </p><p>$

$\text{Rational no. between}\: \frac{1}{7} \text{ \: and \:} \frac{2}{7} \text{\: is \: }</p><p> \\ a) \:\frac{1}{14} \\ \\ b) \:\frac{2}{21} \\ \\ c)\: \frac{5}{14} \\ \\ d) \: \frac{5}{21}$

$\large{\underline{\boxed{\text{Solution:}}}} </p><p>$

First we will multiply the numerator and denominator by 2

$\implies \: \frac{1}{7} \times \frac{2}{2} = \frac{2}{14} \\ \\ \text{similarly} \\ \\ \implies \frac{2}{7} \times \frac{2}{2} = \frac{4}{14}$

Here, only $\: \frac{3}{14}\:$ is possible.

Now,

let's multiply the numerator and denominator by 3

$\implies \: \frac{1}{7} \times \frac{3}{3} = \frac{3}{21} \\ \\ \text{similarly} \\ \\ \implies\: \frac{2}{7} \times \frac{3}{3} = \frac{6}{21}$

Here, $\:\frac{4}{21} \textsf{\:and\:} \frac{5}{21}\:$ are possible.

From the given options $\: \frac{5}{21}\:$ is the required value.

Hence, option d) $\rightarrow \: \boxed{ \frac{5}{21}}\:$ is the answer.