Question

Find five rational number between $ \dfrac{1}{2} $ and $ \dfrac{1}{3} $

Answer 1

Hint: A rational number is the number which can be stated as the ratio of two numbers or which can be expressed as the p/q form or as the quotient or the fraction with non-zero denominator whereas, the numbers which are not represented as the rational are known as the irrational number. Recurring decimal expressions are the expressions or the numbers which are repeated again and again following some pattern like a group of three numbers are repeated again and again and likewise.

Complete step-by-step answer:
Given numbers are: $ \dfrac{1}{2} $ and $ \dfrac{1}{3} $
Now, since the denominator of the above two given rational numbers are different first make the denominators common.
So, to make the common denominators-
Multiply $ \dfrac{1}{2} $ by $ \dfrac{3}{3} $ gives $ \dfrac{3}{6} $ ….. (A)
Now, multiply $ \dfrac{1}{3} $ by $ \dfrac{2}{2} $ gives $ \dfrac{2}{6} $ …. (B)
Now, multiple both the rational numbers by $ \dfrac{6}{6} $
We get the rational number as:
 $ \dfrac{3}{6} \times \dfrac{6}{6} = \dfrac{{18}}{{36}} $
And the other rational number as:
 $ \dfrac{2}{6} \times \dfrac{6}{6} = \dfrac{{12}}{{36}} $
Hence, the rational numbers between the given two numbers are $ \dfrac{{13}}{{36}},\dfrac{{14}}{{36}},\dfrac{{15}}{{36}},\dfrac{{16}}{{36}} $ and $ \dfrac{{17}}{{36}} $
This is the required solution.

Note: Remember the difference between the rational and irrational number. The numbers which are not represented as the rational are known as the irrational number. Always remember that between any two given numbers there are infinite rational and irrational numbers irrespective of how small or large the difference between the two may be. In irrational numbers the numbers in the form of decimal and are the non-repeating and non-terminating numbers. Be good in multiples to get the equivalent values for the fractions.