what is rational number and types with example

 Rational numbers 

# Any number which can be written (or expressed ) in the form of  p/q such that p and q are integer and q is not equal to 0 is called rational number.

For example:- 3, 8/9, -13/5, 0.3, 2.1 etc

Note :   3, 0.3, 2.1 are also rational numbers because they can be written in p/q form as explained below :

3 = 3/1 = p/q form 

0.3 = 3/10 = p/q form 

2.1 = 21/10 = p/q form 

Rational number are two types :

 

 1) Fraction number                                                   2) Decimal number

( Number is p/q form )                                                                        (Number with decimal point )

e.g . 4/5 ,92/3 , 8/16 etc.                                                                     e.g . 0.4 , 5.3 , 52.7 , 6.24 etc. 

Note : All fraction are rational number but all rational number may or may not be fraction .

BASIC ARITHMETIC AND FRACTION

BASIC ARITHMETIC AND FRACTIONS 

INTRODUCTION:-

Basic arithmetic involves the use of various mathematical symbols like '+' '-', etc. in our day to day life we use there symbols to make our decision. similarly fraction are use in our daily life. For example, 'half a kilogram (kg) of sweets means '1/2' in mathematical language.

 

BASIC DEFINITIONS

1. Natural numbers : Natural number are the counting number which starts from 1. 

  Thus 1,2,3,4,............are natural numbers. 

2. Whole numbers : All natural numbers along with zero constitutes whole numbers. in other words, whole number starts from 0,1,2,3,4,.....are whole numbers. 

3. Integers : An integer is a whole number that can be positive (e.g. 1,2,3,4...) or negative (e.g.-1,-2,-3,-4,.....)or zero. Thus -5.-4,0,8,10 etc. are some example of integers. 

4. Even numbers : A whole number which is exactly divisible by 2 is called even number. Thus 2,4,6,8,10,12....even numbers. 

5. Odd numbers : A whole number which is not exactly divisible by 2 is called odd number. Thus 1,3,5,7,9,11,13,....are odd numbers. 

6. Consecutive numbers : The integers in their counting order are called consecutive numbers.

For example ,

(a) 8,9,10,11,12                                           (b) -3,-2,-1,0,1,2,3

7. Prime numbers : A prime number is a natural number greater than 1 which can be divided by itself and by 1only. For example 2 can be divided by 2 and by 1 only. Thus ,2 is a prime number. Other example are 3,5,7,11,19,23.....etc. 

8. Co-prime number : If two numbers do not have a common factor other than 1, they are called co-prime numbers. In other words their H.C.F (Highest common factor) is 1. Example are 

(a) 7 and 10                   (b) 7 and 11                  (c) 11 and 13