Question

Find three rational numbers between $-\dfrac{3}{2}$ and $\dfrac{4}{5}$

Answer 1

Hint: To obtain the three rational numbers we will firstly make the denominator of both the term same i.e. 10 by multiplying and dividing them with a number. Then we will write all the rational numbers that come between the two numbers and get our desired answer.

Complete step by step answer:
We have to find the three rational numbers between the below numbers:
$-\dfrac{3}{2}$ And $\dfrac{4}{5}$
Firstly we will convert the denominator of each number to 10 by multiplying and dividing them with a number.
So first we will multiply and divide the first number by 5 as follows:
$\Rightarrow -\dfrac{3}{2}\times \dfrac{5}{5}$
$\Rightarrow -\dfrac{15}{10}$…..$\left( 1 \right)$
Next we will multiply the second number by 2 as follows:
$\Rightarrow \dfrac{4}{5}\times \dfrac{2}{2}$
$\Rightarrow \dfrac{8}{10}$….$\left( 2 \right)$
From equation (1) and (2) we get two numbers as $-\dfrac{15}{10}$ and $\dfrac{8}{10}$
So the three rational numbers between above two numbers are:
$-\dfrac{7}{10},\dfrac{2}{10},\dfrac{7}{10}$

Note: Rational numbers are those that can be expressed in the form of $\dfrac{p}{q}$ where $q\ne 0$. If it is not a rational number that means it is an irrational number. The set of all rational numbers together with addition and multiplication operations forms a field. The set of a rational number is countable but the set of irrational numbers is uncountable and the real number is a union of rational and irrational numbers so it is also uncountable. If it is not a rational number that means it is an irrational number. In order to find rational numbers between two numbers we should make their denominator equal. It makes it easy to get the rational number as we can just change the numerator and get the desired answer.