# 6 Math Chapter 2 Whole Number

Chapter Notes and Summary
Natural Numbers : Counting numbers are called natural numbers. It is denoted by N.
i.e., N = {1, 2, 3, 4, 5, …}
(i) first and smallest natural number is 1.
(ii) There is no least or greatest natural number.
Whole numbers : All natural numbers together with ‘0’ are called whole numbers. It is denoted by W i.e., W = {0, 1, 2, 3, 4, 5, …}
(i) number 0 is first and smallest whole number.
(ii) All natural numbers are whole numbers. There are infinitely many or uncountable number of whole numbers.
Successor : successor of a whole number is number obtained by adding 1 to it.
Predecessor : predecessor of a whole number is one less than given number.
Operation on whole numbers :
(i) Closure property :
If a and b are any two whole numbers, then (a + b) is also a whole number.
(ii) Commutative law :
If a and b are any two whole numbers, then a + b = b + a.
(iii) Additive property of zero :
If a is any whole number, then a + 0 = 0 + a = a. So, zero is identity for addition of whole numbers.
(iv) Associative law :
If a, b and c are whole numbers,then (a + b) + c = a + (b + c).
Properties of subtraction :
(i) If a and b are two whole numbers such that a > b > 0, then a – b is a whole number, otherwise, subtraction is not possible in whole numbers.
(ii) For any two whole numbers a and b, (a – b) ≠ (b – a).
(iii) For any whole number a, we have a – 0 = a but (0 – a) is not defined in whole numbers.
(iv) If a, b and c are any three whole numbers, then (a – b) – c ≠ a – (b – c).
(v) If a, b and c are whole numbers such that a – b = c, b + c = a.
Properties of multiplication : If a, b and c are three whole numbers, then
(i) Closure property :
(a × b) is also a whole number.
(ii) Commutative law :
a × b = b × a.
(iii) Multiplicative property of zero :
a × 0 = 0 × a = 0.
(iv) Multiplicative property of 1 :
a × 1 = 1 × a = a. So, one is identity for multiplication of whole numbers.
(v) Associative law :
a × (b × c) = (a × b) × c.
(vi) Distributive law of multiplication over addition :
a × (b + c) = (a × b) + (a × c)
(vii) Distribution law of multiplication over subtraction :
a × (b – c) = (a × b) – (a × c) l Properties of division : If a and b are two non-zero whole numbers, then :
(i) a ÷ b is not always a whole number.
(ii) Division by 0 :
a ÷ 0 is meaningless.
(iii) 0 ÷ a = 0.
Number line : In mathematics, a number line is a picture of a gradual straight line that serves as abstraction for whole numbers denoted by W.
To represent whole number on number line, draw a straight line and mark a point on it and label it ‘0’ (zero).
Starting from ‘0’ (zero) on line mark equal intervals (of unit length) to right to 0 and label them as 1, 2, 3, ….
The distance between these points labelled as 0, 1, 2, …is called as unit distance.
The number line for whole numbers is shown as below :
Note : Important and common facts of natural numbers.
• 1 is first and smallest natural number.
• This is not possible that any natural number has no successor.
• There is no predecessor of number 1.
• (Except 1) Every natural number can be found by adding 1 to previous natural number.
• There are infinitely many natural numbers.
• There is no last or greatest natural number.