We have learned about the natural numbers from 1 to 10. Whole numbers are the set natural numbers, including zero. 0 is the smallest whole number. Whole numbers are 0, 1, 2, 3, ……… Allnatural numbers are whole numbers, but all whole numbers are not natural numbers
Properties of Whole Numbers
 Addition and multiplication of any 2 whole numbers give a whole number.
 Subtraction and division of any 2 whole numbers may or may not give a whole number.
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What Is a Number line?
A number line is a picture of a graduated straight and horizontal line in which numbers are written. A number written on the lefthand side of the number line is lesser, and a number written on the righthand side of the number line is greater. Lets us look into some solved example problems.
Find 12 × 35 using distributivity.
12 × 35 = 12 × (30 + 5)
= 12 × 30 +12 × 5
= 360 + 60 = 420.
Calculate – (2 + 3) + 4 = ? = 5+ 4 = 9.
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Evolution of Numbers
Natural Numbers
 Numbers that are used for counting and ordering are called natural numbers.
 1,2,3,4,5,6… are natural numbers
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Whole Numbers
 Natural numbers, along with zero, form the collection of whole numbers.
 0,1,2,3,4,5… are called whole numbers.
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Predecessors and Successors
Predecessor and Successor
 A successor of any number is the next number to it, which is obtained by adding 1.
 A predecessor of any number is the previous number to it, which is obtained by subtracting 1.
 For example, the predecessor and successor of the number 12 is 12 – 1 and 12 + 1, which is 11 and 13
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Where Do Whole Numbers Live?
Number Line
 It is the infinitely long line containing all the whole numbers.
 The line starts at zero, and any two consecutive whole numbers have the same distance between them.
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Describing Number Line
Operations on a Number Line
⇒ Addition on a number line. For example, the addition of 1 and 5 (1 + 5 = 6). First, locate 1 on the number line. Then, moving 5 places to the right will give 6.
⇒ Subtraction on a number line. For example, subtraction of 3 from 7 (7 – 3 = 4). First, locate 7 on the number line. Then move 3 places to the left will give 4.
⇒ Multiplication on a number line. For example, the product of 3 and 4 (3 × 4 = 12). Start from 0 and skip 3 places to the right 4 times.
⇒ Division on a number line. For example, 6 ÷ 3 = 2. Start from 6 and subtract 3 for a number of times till 0 is reached. The number of times 3 is subtracted from gives the quotient.
Properties of Operators: Commutative Associative and Distributive
Division by Zero
Division of any whole number by 0 is not defined.
Mathematical operations are simplified due to certain properties that every number follows. They are:

Commutative Property
Addition and multiplication are commutative for whole numbers, i.e., whole numbers can be added or multiplied in any order.
For e.g: 2 + 3 = 5 = 3 + 3 × 4 = 12 = 4 × 3

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Associative Property
Associativity of addition and multiplication
For eg: (5 +6) + 4 = 15 = 5 + (6 + 4)
(2 × 3) × 4 = 24 =2 × (3 × 4)

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Distributive Property
With distributivity property, 4 × (5 + 3) can be written as (4 × 5) + (4 × 3)
Here, 4 × (5 + 3) = 4 × 13 = 52
Also, (4 × 5) + (4 × 3) = 20 + 32 = 52
There exist certain numbers; when included in mathematical operations like addition and multiplication, the value of the operation remains unchanged. Such numbers are called identities.
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Additive Identity
Additive identity gives the same whole number when added to another whole number.
Zero is the additive identity as a + 0 = a, (a is any whole number).
Multiplicative Identity
Multiplicative identity gives the same whole number when multiplied by another whole number.
1 is the Multiplicative identity as a × 1 = a, (a is any whole number)
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Let’s Play With Whole Numbers
Patterns
 Every number can be arranged as a line.
 E.g : 5 = •••••
 Some whole numbers can be expressed as squares.
 E.g :
 Some whole numbers can be expressed as rectangles.
 E.g : 6 can be shown as 3 × 2
 Some numbers can also be arranged as triangles.
Numbers between Square Numbers
 Between 2 successive square numbers there exists 2n nonsquare numbers. Between n² and (n + 1)², there are nonsquare numbers. Here is a whole number.
 For example, between 9 (3)² and 16 (4)², there are 10 , 11, 12, 13, 14, 15 which is 6 = 2 × 3 numbers.
Adding Odd Numbers
 Sum of the first n natural odd numbers gives n², which is a perfect square.
 For example : Sum of first 5 natural odd numbers ⇒ 1 + 3 + 5 + 7 + 9 = 25 = 5²
Properties of Operators: Closure Properties
Closure Property
Whole numbers are closed under addition and also under multiplication.
3  +  1  =  4, a whole number 
5  +  3  =  8, a whole number 
4  ×  4  =  16, a whole number 
9  ×  2  =  18, a whole number 
Whole numbers are not closed under subtraction and division.
8  –  5  =  3, a whole number 
5  –  8  =  3, not a whole number 
12  ÷  4  =  3, a whole number 
9  ÷  2  =  9/2, not a whole number 
Learn more about the whole numbers from the topics given below:
Real Numbers  Number System 
Whole Numbers  Natural Numbers 
Frequently Asked Questions on CBSE Class 6 Maths Notes Chapter 2 Whole Numbers
What are whole numbers?
A whole number is simply any positive number that does not include a fractional or decimal part.
What are the uses of a number line?
Number line is used as a tool to compare and order numbers and also perform various operations such as addition, subtraction, etc.
What is the ‘Additive identity’ property?
The formula of additive identity is written as a + 0 = a. This explains that when any number is added to zero, the sum is the number itself.
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