Question

Write a rational number which does not lie between numbers $ - \dfrac{2}{3}$ and$ - \dfrac{1}{5}$.

Answer 1

Hint:A Rational numbers are those numbers which is in the form of $\dfrac{p}{q},q \ne 0\left( {p,q \in I} \right)$ where $I$ is the set of integers.Finally we have to find that the given number does not lie in the rational number.

Complete step-by-step answer:
It is given that the rational numbers be $ - \dfrac{2}{3}$ and $ - \dfrac{1}{5}$
We have to find that the rational number which does not lie between numbers $ - \dfrac{2}{3}{\text{ and}} - \dfrac{1}{5}$
First we already know the definition of rational numbers.
Rational numbers are those numbers who are in the form of $\dfrac{p}{q},q \ne 0\left( {p,q \in I} \right)$ where $I$ be the set of integers.
Since we have $ - \dfrac{2}{3}$ and $ - \dfrac{1}{5}$ both negative rational numbers.
Therefore we can choose any rational number which does not lie between the given numbers.
As we know that the two negative numbers cannot have a positive number in between.
Here, the positive number will not be present in the interval $\left( { - \dfrac{2}{3}, - \dfrac{1}{5}} \right)$
Hence we can choose so many numbers which do not lie in the above interval but here the requirement is only one number. So we need to find only that.
So, we can choose randomly a positive rational number, which does not lie in the above interval.
We can choose any positive rational number like $\dfrac{8}{5},\dfrac{4}{3},\dfrac{7}{6}{\text{ and}}\dfrac{9}{8}$ etc.

Note:The number $2$ is also a rational number because in the form of Rational number we can write $2$as $\dfrac{2}{1}$ , In $\dfrac{2}{1}$ numerator is $2$, and denominator is $1$ and $1,2 \in {\text{I}}$.When $1$ is not visible in the denominator but it is there we need to understand because the denominator cannot be $0$, the number would be undefined. The number $0$ is neither a positive rational number nor a negative rational number. There are unlimited rational numbers between two rational numbers.