# Rational Numbers (Definition, Examples)

We have read in detail about natural numbers, whole numbers, integers, and fractions. In this chapter, we will introduce you to a new type of body of numbers, that is, a body of rational numbers.

## Rational numbers

Numbers that are in the form of * p/q*, where p and q are integers and

*, are called rational numbers.*

**q≠0**### Rational Numbers Examples

2/3, 7/8, -2/9, -5/-7, 5/3, 5/2, 5/6, 7/6, 1/3, 10/3, 7/3, 3/7, 8/3, 9/8

## Comment about rational numbers

- Each natural number is a rational number. For example, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are natural numbers. Since these numbers can be written as p / q. 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1 and 9/1. Hence these are rational numbers.
- It is not necessary that each rational number is a natural number. For example, 3/5 is a rational number, but it is not a natural number.
- Since zero (0) can be written as 0/1. Therefore 0 is a rational number.
- Each integer is a rational number. For example, -5 and -7 are integer numbers. Since these numbers can be written as -5/1 and -7/1, these are rational numbers.
- It is not necessary that each rational number is a whole number. For example, 2/3 and 5/2 are rational numbers, but they are not integers.
- Each fraction is a rational number. For example, 5/2 and 6/5 are different. Since, these numbers are in the form of
**p/q**, where p and q are integers and**q ≠ 0**, so they are rational numbers. Thus, in the different**a/b**,**(b ≠ 0)**, a and b are whole numbers. Since every whole number is an integer, so**a/b**is a rational number. - It is not necessary that each rational number by a fraction. For example, 2/-3 is a rational number, since 2 and -3 are integers. But 2/-3 is not a fraction, because -3 is not a whole number.

## Positive and Negative Rational Numbers

A rational number whose numerator and denominator each have the same sign (both positive or both negative) is called a positive rational number.

**For example,** 3/2, 5/2, -5/-3, 6/7, -1/-5, etc. are positive rational numbers.

On the other hand, the rational number whose numerator and denominator of each opposite sign (one positive and the other negative) are called negative rational numbers.

**For example,** -2/3, -3/4, 4/-9, 8/-11, etc. are negative rational numbers.