Question

Find five rational numbers between 1 and 2.

Answer 1

Hint- consider any five numbers between 1 and 2 and convert them into lowest form fraction.

As we know rational numbers are those which are written in the form of $\dfrac{p}{q}$, where $q \ne 0 $and $\dfrac{p}{q}$ is written in lowest form, such that $p$ and $q$ have not no common factors except 1.
For example $\dfrac{2}{3}$ as this fraction is written in lowest form and does not have any common factors except 1, so this is a rational number.
Now we have to find out the rational numbers between 1 and 2
I.e. greater than 1 and less than 2.
So consider five numbers between 1 and 2 which is $\left\{ {1.1,1.2,1.3,1.4,1.5} \right\}$
Now, convert these numbers into fraction
$1.1 = \dfrac{{11}}{{10}},{\text{ }}1.2 = \dfrac{{12}}{{10}},{\text{ }}1.3 = \dfrac{{13}}{{10}},{\text{ }}1.4 = \dfrac{{14}}{{10}},{\text{ }}1.5 = \dfrac{{15}}{{10}},$
Now, convert these fraction into lowest form such that these fraction have not any common factors
$
   \Rightarrow 1.1 = \dfrac{{11}}{{10}} \\
   \Rightarrow 1.2 = \dfrac{{12}}{{10}} = \dfrac{6}{5} \\
   \Rightarrow 1.3 = \dfrac{{13}}{{10}} \\
   \Rightarrow 1.4 = \dfrac{{14}}{{10}} = \dfrac{7}{5} \\
   \Rightarrow 1.5 = \dfrac{{15}}{{10}} = \dfrac{3}{2} \\
$
So, $\left\{ {\dfrac{{11}}{{10}},\dfrac{6}{5},\dfrac{{13}}{{10}},\dfrac{7}{5},\dfrac{3}{2}} \right\}$ are the required five rational numbers between 1 and 2.

Note: - In such types of problems the key concept we have to remember is that always remember the condition of rational number which is stated above, then assume any five numbers between 1 and 2, then convert them into fraction then convert them into lowest form fraction such that the fractions have not any common factors, then we will get the required answer.