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Maths / Rational Numbers / Rational Numbers
(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

## Rational Numbers

The various numbers can be classified into various categories such as:

### Natural Numbers:

The group of numbers staring from 1 and going to infinity are known as natural numbers. They are also called counting numbers. The can be expressed as

1,2,3,4,.....,

### Whole Numbers :

The group of numbers formed by including 0 to the group of natural numbers, are known as whole numbers. Such as  0, 1, 2, 3, 4, ......

### Integers:

The group of numbers formed by adding the negative of natural numbers to the group of whole numbers is known as a group of integers. The integers are .,...-4, -3, -2, -1, 0 1, 2, 3, 4, and so on. They can be represented on a number line as

Addition, subtraction, multiplication and division operations were done on integers and various properties (Closure property, Commutativity, Associativity, Existence of identity, Existence of inverse) of these operations were discussed.

• 1,2,3,4,..... are known as positive integers
• -1, -2, -3, -4, .... are known as negative integers
• 0 is neither negative nor positive.
• ### Rational Numbers:

As you can see that we can place infinite number of points between to integers on a number line. some of these numbers are called fractions. For example if we divide 3 by 2 we get 3/2 which is a fraction. All these fractions along with integers are known as rational numbers.this group is represented by (Q)

Any number that can be represented in the form  $\frac{p}{q}$ where p and q are co-prime integers, the numerator p and the denominator q can be any integers  but  $q\neq 0$, is called a rational number. The examples of rational numbers will be $\frac{1}{5}, \frac{-7}{9}, \frac{45}{7}\;\;etc$.

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