# Rational Number Between Two Rational Numbers

A rational number is a number which can be written in the form of \(p/q\)

Let us first go through some of the examples and then learn how to find rational numbers between two other rational numbers.

## Finding Rational Numbers between Two Rational Number

- The simplest method to find a rational number between two rational numbers
*x*and*y*is to divide their sum by 2.

Example: \(\frac{3}{1}~and~\frac{4}{1}\)

Example: For numbers with common denominator like \(\frac{3}{20}~and~\frac{9}{20}\)

- For a negative and a positive number like \(\frac{-3}{20}~and~\frac{3}{20}\)
, we have \(\frac{-2}{20},~ \frac{-1}{20},~\frac{0}{20},~\frac{1}{20},~\frac{2}{20}\) , etc. - We can write \(\frac{3}{20}\)
as \(\frac{30}{200}\) and \(\frac{9}{20}\) as \(\frac{90}{200}\) . Thus, rational number between \(\frac{3}{20}~and~\frac{9}{20}\) can also be \(\frac{31}{200},~ \frac{32}{200},~\frac{33}{200},~\frac{34}{200},……..~\frac{89}{200}\) and so on . - For finding rational numbers between two rational numbers with different denominators, we first find their equivalent fraction with the same denominator and then find the rational number between them. For example, for finding numbers between \(\frac{-1}{3}~and~\frac{5}{9}\)
. , we convert \(\frac{-1}{3}~to~\frac{-1\times 3}{3 \times 3}=\frac{-3}{9}\) . Now, we have \(\frac{-2}{9},~ \frac{-1}{9},~\frac{0}{9},~\frac{1}{9},~\frac{2}{9},~\frac{3}{9},~\frac{4}{9}\) between them.

Rational number form one of the major part of mathematics and one cannot deny the importance of mathematics in today’s world.