Question

Find a rational number between $-1$ and $\dfrac{1}{2}$

Answer 1

Hint: For the type of question in which the rational number is asked between any two numbers, first look at the number of rational numbers they had asked. In our case a single rational number is asked. For finding a one rational number between any two numbers just find the average of these two values. The outcome will be the answer.

Complete step by step answer:
But if more than one rational number is asked then you need to make the value in p/q form. By multiplying or dividing with some reasonable number, based on the rational number we need to find out. For example, $-1$ and $\dfrac{1}{\begin{align}
  & 2 \\
 & \\
\end{align}}$ can also be written as $-\dfrac{20}{20}$and $\dfrac{10}{20}$. In which we can easily find the number between these values.
For our question a rational value between $-1$ and $\dfrac{1}{2}$.
By first method
Rational number between $-1$ and \[\dfrac{1}{2}\]$=\dfrac{1}{2}\left( -1+\dfrac{1}{2} \right)$
Rational number between $-1$ and \[\dfrac{1}{2}\]$=\dfrac{1}{2}\left( -\dfrac{1}{2} \right)$
Rational number between $-1$ and \[\dfrac{1}{2}\]$=-\dfrac{1}{4}$
So $-\dfrac{1}{4}$ is one of the rational number between $-1$ and \[\dfrac{1}{2}\]

By method 2
Rational number between $-1$ and \[\dfrac{1}{2}\]
So multiply the value by a number such that both values have the same denominator, and the value should be clearly seen large so that you can easily find out the rational number between them. Let you multiply and divide by 20 in $-1$ and 10 in $-\dfrac{1}{2}$ so that both will have the same denominator.
So the values we will get will be $-1\times \dfrac{20}{20}=-\dfrac{20}{20}$ and $\dfrac{1}{2}\times \dfrac{10}{10}=\dfrac{10}{20}$
So the value will be $-\dfrac{20}{20}$ and $\dfrac{10}{20}$
So now to find out a rational number between it, it can be any of $-\dfrac{19}{20},-\dfrac{18}{20},-\dfrac{17}{20}............\dfrac{9}{20}$ all will be the answer of this question. And you can write any one of them. However, between these numbers of value $-\dfrac{5}{20}$ also exist, which can further be simplified to $-\dfrac{1}{4}$ which we got through the first method.

Note: First method is only valid when you need to find one rational number. But if you want to find a more rational number then you can go with the second method. Keep in mind that for the second method denominators need to be the same of two values.