Rational Numbers, Properties, Operations
How to find the rational numbers between two rational numbers?
There are infinite numbers of rational numbers between two rational numbers. The rational numbers between two rational numbers can be found easily using two different methods. Now, let us have a look at the two different methods.
Method 1:
Convert the denominator as same denominator for given rational numbers. Then we can write rational numbers between them.
Ex : Find rational number between \(
\frac{1}
{4}
\) and \(
\frac{1}
{2}
\) .
Solution: Let \(
\frac{1}
{4}
\) ,\(
\frac{1}
{2}
\)
\(
\begin{gathered}
\Rightarrow \frac{{1 \times 2}}
{{4 \times 2}},\frac{{1 \times 4}}
{{2 \times 4}} \hfill \\
\Rightarrow \frac{2}
{8},\frac{4}
{8} \hfill \\
\end{gathered}
\)
\(
\frac{3}
{8}
\) is between \(
\frac{2}
{8}\& \frac{4}
{8}
\)
\(
\therefore \frac{2}
{8},\frac{3}
{8},\frac{4}
{8}
\)
Method 2:
Mean value for the given two rational numbers lies between them which is required rational number.
If we want to find more numbers repeat the same process with the old & newly obtained rational number.
Ex : Find rational number between \(
\frac{3}
{4}\& \frac{1}
{2}
\)
Solution : Rational number between \(
\frac{3}
{4}\& \frac{1}
{2}
\) is
\(
\frac{{\frac{3}
{4} + \frac{1}
{2}}}
{2} = \frac{{\frac{{3 + 2}}
{4}}}
{2} = \frac{5}
{8}
\)
\(
\therefore \frac{5}
{8}
\) lies between \(
\frac{3}
{4}\& \frac{1}
{2}
\)