Question

Find the four rational numbers between -1 and 0.

Answer 1

Hint: Convert the two numbers in the equivalent fraction by multiplying and dividing each number by \[\left( n+1 \right),\]where n is the number of required rational numbers.

Complete step by step solution:
In the question, we have to find the four rational numbers between -1 and 0.
So here we will divide and multiply -1 with \[\left( 4+1=5 \right)\]to get the fraction given as:
\[\begin{align}
  & \Rightarrow -1=\dfrac{-1\times 5}{5} \\
 & \Rightarrow -1=\dfrac{-5}{5} \\
\end{align}\]
Next, we will do the same with 0, and we get:
\[\begin{align}
  & \Rightarrow 0=\dfrac{0\times 5}{5} \\
 & \Rightarrow 0=\dfrac{0}{5} \\
\end{align}\]
Now, we can take any four fractions between \[\dfrac{-5}{5}\] and \[\dfrac{0}{5}\] , as follows:
\[\dfrac{-4}{5}\], \[\dfrac{-3}{5}\], \[\dfrac{-2}{5}\]and \[\dfrac{-1}{5}\].
All these fractions are rational numbers and lie between \[\dfrac{-5}{5}=-1\] and \[\dfrac{0}{5}=0\].
So the four required rational numbers are:
\[\dfrac{-4}{5}\], \[\dfrac{-3}{5}\], \[\dfrac{-2}{5}\]and \[\dfrac{-1}{5}\].


Note: The denominator has to be the same for the two equivalent fractions of the two numbers so formed. The alternate method to find the rational number between two numbers will be finding the average of the two numbers. This way we will get the one rational between two given numbers. Then again taking the average of the first number and the rational number formed above to get the second rational number between them and so on.