Ch-2 Whole Number Quick revision Notes | Class 6 Maths | edugrown

Whole Numbers

• On adding the predecessor of 1, i.e., 0 in the queue of natural numbers, we get the whole number.
• 0,1,2,3,4,5……. are whole numbers.
• All whole numbers are natural numbers but all natural numbers are not whole numbers.

The Number Line

• The whole numbers are shown on the number line as shown below

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• The number line shows that the number on the right side of the other number is the greater number.
• The number line shows that the number on the left side of the other number is the smaller number.

Adding on the Number Line: 

• Suppose a+b is to be found from the number line. Then mark a unit on the number line and move the b units towards the right of a. 
• For example: The addition of 2 and 3 

Move 3 units towards the right of 2, we will get 5 

Subtracting on the Number Line:

• Suppose a−b is to be found from the number line then mark a on the number line then move b unit towards the left of a 
• For example: The subtraction of 5 and 3 

Move 3 units towards the left of 5, we will get 2 

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Properties of the Whole Number

1. Closure Property

• The whole numbers are closed under addition means the sum of two whole numbers is always a whole number.

For example: 5 and 8 are whole numbers and their sum 13 is also a whole number. 

• The whole numbers are also closed under multiplication, which means the multiplication of two whole numbers is always a whole number.

For example: 5 and 8 are whole numbers and their multiplication 40 is also a whole number. 

2. Commutative Property

• Whole numbers are commutative under addition. It means that they can be added in any order and the result will be the same.

For example: 4+2=6 and 2+4=6. 

• Whole numbers are also commutative under multiplication. It means that they can be multiplied in any order and the result will be the same.

For example: 5×3=15 and 3×5=15.

3. Associative Property 

• Whole numbers are associative under addition means rearranging the whole number in parenthesis and then adding will not affect the answer. 

For example: 

(12+5)+6

=17+6 

=23   

And 

12+(5+6) 

=12+11 

=23

• Whole numbers are associative under multiplication means rearranging the whole number in parenthesis and then multiplying will not affect the answer. 

For example: 

(2×5)×3

=10×3 

=30   

And 

2×(5×3) 

=2×15 

=30 

4. Distributivity of Multiplication Over Addition

• When a whole number is multiplied by the sum of the whole number then the distributive property of multiplication over addition is used. 

For example: 

8×(5+2) 

=(8×5)+(8×2) 

=40+16 

=56 

5. Additive Identity

• If adding 0 to any whole number gives the whole number itself, then 0 is the additive identity. 

For example: 9+0=9 

6. Multiplicative Identity

• If multiplying 1 to any whole number gives the whole number itself, then 1 is the multiplicative identity. 

For example: 6×1=6