Question

Write any $ 3 $ rational numbers between $ - 2 $ and $ 0 $ ?

Answer 1

Hint: A rational can be written in the form of $ \dfrac{p}{q} $ here p and q are two integers and $ q \ne 0 $ . In the given question two rational numbers are given, there exists an infinite number of rational numbers between them. In which we have to find 3 rational numbers.
We first check the denominator of both numbers. “If both the denominators are equal then we compare the numerators. If numerators differ by large number, then we add any small constant integer value to the smaller numerator, keeping the denominator same and if numerators differ by smaller number then we multiply both the rational number by a large constant value after that we add small constant integer to the smaller numerator”.

Complete step-by-step answer:
In the given problem
We have to find $ 3 $ rational number between $ - 2 $ and $ 0 $ .
We can also write $ - 2 $ and $ 0 $ as \[\dfrac{{ - 2}}{1}\] and $ \dfrac{0}{1} $ .
Since the denominator of both numbers are equal and we have to find $ 3 $ rational number between given numbers
So we multiply numerator and denominator of both numbers by 4, we get
 $ \dfrac{{ - 2 \times 4}}{{1 \times 4}} = \dfrac{{ - 8}}{4} $
 $ \dfrac{{0 \times 4}}{{1 \times 4}} = \dfrac{0}{4} $
Now we add $ 1 $ to the smaller numerator $ - 8 $ , we get
\[\dfrac{{ - 8 + 1}}{4} = \dfrac{{ - 7}}{4}\]
And by successive adding $ 1 $ to the numerator we get the required rational numbers
 $ \dfrac{{ - 7 + 1}}{4} = \dfrac{{ - 6}}{4} = \dfrac{{ - 3}}{2} $
and $ \dfrac{{ - 3 + 1}}{2} = \dfrac{{ - 2}}{2} = - 1 $
Hence required $ 3 $ rational numbers are $ \dfrac{{ - 7}}{4},\dfrac{{ - 3}}{2} $ and $ - 1 $ .

Note: In this type of question If both the denominator are not equal then we first make both the denominator equal by taking LCM or by successive multiplication of denominators of any one of the fraction to both the numerator and denominator of other such that the denominators become same. Then we follow the above step.