# Find five rational numbers between 1 and 2.

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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.

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.

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