Rational Numbers:

Rational numbers are those numbers that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. In other words, any number that can be represented as a fraction is a rational number. Rational numbers include both positive and negative numbers, as well as zero.

Examples of rational numbers include 1/2, -3/4, 0, 5, and -7.

Understanding Natural Numbers, Whole Numbers and Integers:

Natural numbers are the counting numbers, such as 1, 2, 3, 4, 5, and so on. These numbers are used to count objects or to represent the position of an object in a sequence.

Whole numbers include all the natural numbers along with zero. So, the set of whole numbers is {0, 1, 2, 3, 4, 5, ...}.

Integers include all the whole numbers along with their negatives. So, the set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Rational numbers are a subset of the real numbers, which include all the numbers that can be represented on a number line. Real numbers include both rational and irrational numbers, such as pi (π) and √2.

Properties of Rational Numbers:

Rational numbers have several properties that make them useful in mathematical operations. Some of these properties include:

- Closure Property: The sum or product of two rational numbers is always a rational number.
- Commutative Property: The order of addition or multiplication does not affect the result.
- Associative Property: The grouping of numbers in addition or multiplication does not affect the result.
- Identity Property: The sum of any rational number and zero is the same rational number, and the product of any rational number and 1 is the same rational number.
- Inverse Property: Every rational number has an additive inverse (a number that when added to the original number equals zero) and a multiplicative inverse (a number that when multiplied by the original number equals 1).

Conclusion:

Rational numbers are an important part of mathematics and are used in a variety of fields, including science, engineering, and economics. Understanding the properties and characteristics of rational numbers can help students develop a strong foundation in mathematics and prepare them for more advanced topics.

Rational no.s are the no.s in which they are always in fraction . if the no. is not in fraction then they are not rational no.s