# 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 q≠0, are called rational numbers.

### 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 1. 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.
2. 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.
3. Since zero (0) can be written as 0/1. Therefore 0 is a rational number.
4. 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.
5. 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.
6. 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.
7. 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.