Question

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

Answer 1

Hint: We are asked to find the rational number between the two fractions. Fractions are the part of the whole. Usually, it represents any number of equal parts and it defines the part from a certain size. Here first we will find the rational numbers between the two.

Complete step-by-step answer:
A rational number is the number which can be well defined as the ratio of two numbers or which can be expressed as the p/q form or as the quotient or the fraction which are with non-zero denominators.
Find the equivalent fraction for the given two fractions.
 $ \dfrac{1}{2} = \dfrac{{1 \times 3}}{{2 \times 3}} = \dfrac{3}{6} $ …. (A)
And $ \dfrac{2}{3} = \dfrac{{2 \times 2}}{{3 \times 2}} = \dfrac{4}{6} $ …. (B)
When you do not get the required number of rational numbers, then first of all find the equivalent fraction for the given fractions and then start getting the rational numbers between the two.
So, Multiply the equation (A) and (B) with the fraction $ \dfrac{6}{6} $
 $ \dfrac{3}{6} \times \dfrac{6}{6} = \dfrac{{18}}{{36}} $ …. (C)
And $ \dfrac{4}{6} \times \dfrac{6}{6} = \dfrac{{24}}{{36}} $ …. (D)
Now the four required rational numbers between the given two numbers are -
 $ \dfrac{{19}}{{36}},{\text{ }}\dfrac{{20}}{{36}},{\text{ }}\dfrac{{21}}{{36}},{\text{ }}\dfrac{{22}}{{36}} $

Note: Remember the difference between the rational and irrational number. The numbers which are not denoted as the rational are known as the irrational number. Always remember that between any two given numbers there are infinite rational and irrational numbers regardless of how small or large the difference between the two numbers 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 and finding the equivalent values for the fractions.