Question

List five rational numbers between \[-2\] and \[-1\] .

Answer 1

Hint: In this question first we multiply and divide given numbers by a common number then we can easily write a rational number between those two numbers.
Rational number: The numbers which can be written in the \[\dfrac{p}{q}\] form (and where \[q\ne 0\]) are called Rational numbers.
Example: \[-5=\dfrac{-5}{1}\](i.e \[p=-5,q=1,q\ne 0\])
\[\Rightarrow 0=\dfrac{0}{1}\] (i.e \[p=0,q=1,q\ne 0\])
\[\Rightarrow 7=\dfrac{7}{1}\] (i.e \[p=7,q=1,q\ne 0\])

Complete step-by-step solution -
Now, let's solve the problem.
We have to list five rational number between \[-2\] and \[-1\]
Okay:
We all know that “if we multiply a number (say p) with some number (say q) and divide them with the same number (q); then the original number (p) won’t change.”
Mathematically;
Let \[p\to \] original number
\[q\to \] same number
Now, \[p=p\times \dfrac{q}{q}\]
\[\Rightarrow p\times 1\]
\[\Rightarrow p\]
Example: \[7=7\times \dfrac{9}{9}\]
\[\Rightarrow 7\times 1\]
\[\Rightarrow 7\]
In the given question we have to find five rational numbers between \[-2\] and \[-1\]
So, the logic is we have to multiply and divide the both numbers with same number so that the difference between both numbers’s numerator is not less than 5 (i.e. at least )
Now, I will choose a number \[10\]
Now we can multiply and divide $10$ in $-2$ . So we can write
 \[\Rightarrow -2=-2\times \dfrac{10}{10}\]
\[\Rightarrow \dfrac{-20}{10}\]
Similarly we can multiply and divide $10$ in $-1$ . So we can write
\[\Rightarrow -1=-1\times \dfrac{10}{10}\]
\[\Rightarrow \dfrac{-10}{10}\]
And difference between two numbers numerators is
\[\Rightarrow -10-(-20)\]
\[\Rightarrow 10(>5)\]
So; \[\dfrac{-11}{10},\dfrac{-12}{10},\dfrac{-13}{10},\dfrac{-14}{10},\dfrac{-15}{10},\dfrac{-16}{10},\dfrac{-17}{10},\dfrac{-18}{10},\dfrac{-19}{10}\] are the rational numbers between \[-1\And -2\]
Therefore, the rational number between \[-1\] and \[-2\] are \[\dfrac{-11}{10},\dfrac{-12}{10},\dfrac{-13}{10},\dfrac{-14}{10},\dfrac{-15}{10}\].

Note: So finally any problem based on the above concept can be done easily. Remember we have to multiply and divide the given numbers with a number (same number). So that the difference between the numerators of both numbers is greater than or equal to the required range mentioned in the question.