Numbers

There are two types of Numbers.                                                        

1. Real Numbers

2. Complex Numbers (Real numbers + Imaginary Numbers)

Real Numbers: The numbers which can be represented on the number line by a unique point are called real numbers. 

Examples: -1, -2, -3, -4 ....................... , and 1, 2, 3, 4, 5.........................  

Complex Numbers: Coplex numbers are the numbers which consist of both real and Imaginary numbers.

Examples: 2 + i√3, where 2 is real part and i√3 is imaginary part. 

 

Real Numbers

(A)  Rational Numbers: The numbers which can be express in the form of p/q, and q≠0 such a numbers are known as real numbers. 

(B)  Irrational Numbers: The numbers which are not rational numbers but these an be represented on a number line, such numbers are known as irrational numbers. 

 

Rational Numbers

(I)  Integers:

      (a) Whole numbers: These are the set of positive integers from 0. Which                  have not decimal and fractional part. Such numbers are known as                        whole numbers.

           Example: 0, 1, 2, 3, 4, 5, ........................... 

           (i)  Natural Numbers: Natural numbers counting begin from 1 to ∞                             (infinty). such numbers are called natural numbers. 

                Ex: 1, 2, 3, 4, 5 ....................................... ∞. 

          (ii) Zero: 0 

      (b) Negative integers: The numbers before 0 on number line is called as                 negative integers these are -1, -2, -3, -4 ............................. -∞. 

(II) Fractional Numbers: 

      (a) Proper fraction

      (b) Improper fraction

 

Natural numbers

(a) Odd Numbers: The numbers which can not be divided by 2 are called odd           numbers. 

      Example: 1, 3, 5, 7, 9, 11, 13, 15 ................................................. ∞. 

(b) Even Numbers: The numbers which can be divided by 2 are called even             numbers. 

      Example: 2, 4, 6, 8, 10, 12, 14, 16 ................................................ ∞. 

(c) Prime Numbers:

(d) Composite Numbers:

(e) Co-prime Numbers:

(f)  Perfect Numbers:

 

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Q1. एक कक्षा के 20 लडके तथा 15 लड़कियों को n वर्गों में इस प्रकार बाँटा गया कि प्रत्येक वर्ग में x लडके तथा y लड़कियाँ राखी गई | x, y तथा n के मान ज्ञात कीजिए | कक्षा में किन मूल्यों का प्रदर्शन किया गया ? 

A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Find x, y and n. What values are reffered in a class ?

solution: 

HCF of 20 and 15 = 5 

so number of groups = 5

 ∴ Number of students in each group (n) = (20 + 15)/5 = 7 

n =7 

Hence, x = 20/5 = 4 boys

y = 15/5 = 3 girls. 

Value : Promote co-education, Promote and help to educate girl child, Role of activity in groups.

Q2. यदि d, 40 और 65 का HCF है तो, पूर्णांकों x और y के ऐसे मान  ज्ञात कीजिए, जो कि d = 40x + 65y को संतुष्ट करते है | 

if d is the HCF of 40 and 65, find the value of integers x and y which satisfiy d = 40x + 65y.