Question

Find the four rational numbers between 1 and 2.

Answer 1

Hint: We solve this problem by using the definition of a rational number.
A number that is represented in the form \[\dfrac{p}{q}\] where, \[q\ne 0\] is called a rational number.
We use the condition that if we add a number \[n\] to rational numbers between 0 and 1 then the resultant numbers will lie between \[n\] and \[n+1\]
By using the above definition we find the rational numbers that lie between 0 and 1 so that we get a rational number between 1 and 2 by adding 1 to those numbers.

Complete answer:
We are asked to find the rational numbers between 1 and 2.
First let us find the rational numbers between 0 and 1.
We know that a number that is represented in the form \[\dfrac{p}{q}\] where, \[q\ne 0\] is called a rational number.
We know that increasing the denominator of 1 to more than 1 then the number lie between 0 and 1
By using the above two condition we get the rational numbers that lie between 0 and 1 as
\[\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}\]
We know that if we add a number \[n\] to rational numbers between 0 and 1 then the resultant numbers will lie between \[n\] and \[n+1\]
We are asked to find the rational numbers between 1 and 2
So, let us add 1 to the above rational numbers between 0 and 1 then we get
\[\Rightarrow \dfrac{1}{2}+1=\dfrac{3}{2}\]
\[\Rightarrow \dfrac{1}{3}+1=\dfrac{4}{3}\]
\[\Rightarrow \dfrac{1}{4}+1=\dfrac{5}{4}\]
\[\Rightarrow \dfrac{1}{5}+1=\dfrac{6}{5}\]
Therefore we can conclude that the rational numbers between 1 and 2 are given as
\[\dfrac{3}{2},\dfrac{4}{3},\dfrac{5}{4},\dfrac{6}{5}\]

Note:
Students may do mistake in understanding the term between
We are asked to find the rational numbers between 1 and 2
We know that 1 and 2 are also rational numbers but we cannot give them an answer for this question.
This is because the term between 1and 2 indicates that not to include 1and 2
But students may give 1 and 2 are also rational numbers between 1and 2 which is wrong.