Natural Numbers and Whole Numbers

Chap 1

Natural Numbers and Whole Numbers

Some Important facts:

1.    Natural numbers : Natural Numbers  are those numbers which start from 1 and go upto endless numbers. e.g. 1, 2, 3, 4, 5, 6……..

2.    By adding 1 to a natural number, we get the next natural number known as its successor.

3.    By subtracting 1 from any natural number (other than 1) we get a natural number preceding the number known as its predecessor.

4.    Number ZERO (0) fractional number (1/2,3/5 etc.) and decimals (1.5,2.1,3.07 etc.) are not natural numbers.

5.    The numbers 0, 1, 2, 3, 4 …etc., obtained by including 0 with the natural numbers, are called whole numbers.

6.    Natural and whole numbers are unlimited in numbers.

7.    For any two whole numbers a and b either (i) a<b or (ii) a=b or (iii) a>b.

8.    The sum of two whole numbers is always a whole number.

9.    If a and b are two whole numbers, then a + b = b + a.

10.   If a,b,c are three whole numbers, then (a+b)+c = a+(b+c)

11.   Numbers 0 is a whole number that for any whole number                   

     a;a + 0 = a = 0 + a.

12.   If a = b, then a-b = 0

13.   If b = 0, then a-b = a viz a – 0 = a

14.   For every whole number a ; a – a = 0

15.   If a,b,c, are three whole numbers and c ≠ 0 then                                     

    a – (b – c), ≠ (a – b) – c

16.    If a, b, c are three whole numbers such that a-b = c then b + c = a.

17.   a x 0 = 0 x a = 0 for every whole number a.

18.   The product of two whole numbers is always a whole number.

19.   If a and b are two whole numbers then a x b = b x a.

20.   If a, b and c are three whole numbers then

          (a x b) x c = a x (b x c)

21.   The whole number 1 is such that a x 1 = 1 x a = a, for every whole number a

22.   For any three whole numbers a, b and c

      a x (b x c) = a x b + a x c

and    (b + c) x a = b x a + c x a

23.      For any three numbers a, b and c if b>c then

      a x (b - c) = a x b – a x c

and    (b - c) x a = b x a – c x a

24.      If a, b and c are three whole numbers such a>b and c ≠ 0 then    (a x c) > (b x c).

25.     If a and b are two whole numbers (b ≠ 0) then (a ÷ b) may or may not be a whole number.

26.     Division by 0 is a meaningless operation.

27.     Let a, b and c be three whole numbers such that b ≠ 0 and c ≠ 0.

(i)            If a ÷ b = c then b x c = a

(ii)          If b x c = a then a ÷ c = b and a ÷ b = c.

28.        If a is any whole number except ZERO, then a ÷ a = 1.

29.       For any whole number a; a ÷ 1 = a.

30.       0 is such a whole number that for any other whole number a ≠ 0 ; 0    

         ÷ a = 0.

31.       Law of Division:-

Dividend = Divisor x Quotient + Remainder.