**Important Concepts and Formulas**

1. Numbers such as 1, 2, 3, 4, 5, 6, …
are called natural numbers. The smallest natural number is 1 and the greatest
natural number does not exist.

To study in detail ------ Click Here!

To study in detail ------ Click Here!

2. The natural numbers along with ‘0’
form the collection of whole numbers. ‘0’ is the smallest whole number. The greatest
whole number does not exist.

3. Properties of addition of whole
numbers:

·
Closure
Property: (a + b) or (b + c) or (a + c) is a whole number. For example, 5 + 8 =
13

·
Commutative
Property: a + b = b + a For example, 4 + 3 = 7 = 3 + 4

·
Associative
Property: (a + b) + c = a + (b + c) For example, 2 + (3 + 7) = (2 + 3) + 7 = 12

·
Additive
Identity: a + 0 = a = 0 + a ‘0’ is called the additive identity for whole
numbers. For example, 6 + 0 = 6 = 0 +6

4. Properties of subtraction of whole
numbers:

·
a
– b is not always a whole number. For example, 5 – 8 = -3. Subtraction is not
closed for whole numbers.

·
Subtraction
is not commutative. a – b ≠ b – a. For example, 3 – 2 ≠ 2 – 3

·
Subtraction
is not associative for whole numbers. For example, (5 – 4) – 3 ≠ 5 – (4 – 3)

·
a
– 0 = a. For example, 5 – 0 = 5. This is known as the property of 0 for
subtraction of whole numbers.

5. Properties of multiplication of whole
numbers:

·
Closure
Property: a × b or b × c is a whole number. For example, 5 × 7 = 35

·
Commutative
Property of Multiplication: a × b = b × a For example, 5 × 8 = 8 × 5

·
Identity
Property of Multiplication: a × 1 = a

·
Zero
Property of Multiplication: a × 0 = 0

·
Associative
Property of Multiplication: (a × b) × c = a × (b × c) For example, (2 × 3) × 7
= 2 × (3 × 7)

·
Distributive
Property of Multiplication: a × (b + c) = a × b + a × c For example, 9 × (3 +
2) = 9 × 3 + 9 × 2

6. Properties of division of whole
numbers:

·
a
÷ b is not always a whole number. For example, 13 ÷ 2 = decimal number. Division
is not closed for whole numbers

·
Division
is not commutative for whole numbers. a ÷ b ≠ b ÷ a. For example, 10 ÷ 5 ≠ 5 ÷
10

·
Division
is not associative for whole numbers. For example, (10 ÷ 5) ÷ 2 ≠ 10 ÷ (5 ÷ 2)

·
Identity
Property of Division: a ÷ 1 = a

·
Zero
Property of Division: 0 ÷ a = 0, where a ≠ 0

7. Patterns in numbers are useful for
verbal calculations.

·
Number
of dots such as 6, 8, 12, etc., can be arranged as a rectangle.

·
Number
of dots such as 4, 9, 16, 25, etc., are called square numbers.

·
Number
of dots such as 3, 6, 10, etc., can be arranged as a triangle.