Question

What rational number is between $ - \dfrac{2}{6}$ and $ - \dfrac{1}{6}$?

Answer 1

Hint: We can find a rational number between $ - \dfrac{2}{6}$ and $ - \dfrac{1}{6}$ by finding the average between the two rational numbers. To find the average between the two rational numbers we will add the two numbers first and then divide the sum by $2$to get the rational number between the given two rational numbers. We will get the number exactly at the middle of the two rational numbers. So, let us see how to solve this problem.

Complete step by step answer:
The given two rational numbers are, $ - \dfrac{2}{6}$ and $ - \dfrac{1}{6}$. To find a rational number between the two rational numbers, we will find the average of the two numbers.So, to find the average we will find the sum between the two numbers first, that is,
$\Rightarrow \left( { - \dfrac{2}{6}} \right) + \left( { - \dfrac{1}{6}} \right) = - \dfrac{3}{6}$
Now, to find the average we will divide the sum by $2$.
Therefore, the average is, $\dfrac{{ - \dfrac{3}{6}}}{2}$
$\Rightarrow - \dfrac{3}{{12}} = - \dfrac{1}{4}$

Therefore, the rational number between $ - \dfrac{2}{6}$ and $ - \dfrac{1}{6}$ is $ - \dfrac{1}{4}$.

Note: We can find infinitely many rational numbers between $ - \dfrac{2}{6}$ and $ - \dfrac{1}{6}$. There are infinitely many numbers, we can simply just keep on writing the numbers. We can find the other numbers by finding the sum by dividing it by natural numbers like $2,3,4,.....$. Then also, we can find other rational numbers by taking the in between rational numbers and finding the sum of the rational number given and the one found and again dividing it by $2$. We can keep on doing so and find many other numbers like this. We should know the formula for finding the average of given numbers as ${\text{Average = }}\dfrac{{{\text{Sum of numbers}}}}{{{\text{Total number}}}}$.