- Properties of Whole Numbers :Additive Properties (Properties due to Addition):
a) Closure Property of Addition: The Set of Whole Numbers is closed with respect to the operation of Addition. In general, it means that the sum of Whole Numbers is always a Whole Number.
This is known as Closure Property of Addition in the Set of Whole Numbers.
For example: 3 and 5 are two Whole Numbers, then 3 + 5 = 8 is also a Whole Number.
- b) Commutative Law of Addition: If a and b are two Whole Numbers, then
a + b = b + a.
This is known as Commutative Law of Addition in the Set of Whole Numbers.
For example: 3 and 5 are two Whole Numbers, then
3 + 5 = 8
&
5 + 3 = 8
Hence, it is established that, 3 + 5 = 5 + 3
- c) Associative Law of Addition: If a, b and c are three Whole Numbers, then
a + (b + c) = (a + b) + c
This is known as Associative Law of Addition in the Set of Whole Numbers.
For example: 3, 5 and 7 are three Whole Numbers then
3 + (5 + 7) = 3 + 12
= 15
&
(3 + 5) + 7 = 8 + 7
= 15
Hence, it is established that, 3 + (5 + 7) = (3 + 5) + 7
- d) Existence of Additive Identity: For every Whole Number a, there exist a unique Whole Number 0 (Zero) such that
0 + a = a + 0 = a
0 (Zero) iscalled the Additive Identity in the Set of
Whole Numbers For example: Let us consider a Whole Number 5. Then we have,
0 + 5 = 5 + 0 = 5
- Multiplicative Properties (Properties due to Multiplications):
- a) Closure Property of Multiplication: The Set of Whole Numbers is closed with respect to the operation of Multiplication. In general, it means that the Product of Whole Numbers is always a Whole Number.
This is known as Closure Property of Multiplication in the Set of Whole Numbers.
For example: 3 and 5 are two Whole Numbers, and then 3 × 5 = 15 is also a Whole Number.
Also Read Properties of Natural Numbers
- b) Commutative Law of Multiplication: If a and b are two Whole Numbers, then
a × b = b × a.
This is known as Commutative Law of Multiplication in the Set of Whole Numbers.
For example: 3 and 5 are two Whole Numbers, then
3 × 5 = 15
&
5 × 3 = 15
Hence, it is established that, 3 × 5 = 5 × 3
- c) Associative Law of Multiplication: If a, b and c are three Whole Numbers, then
a × (b × c) = (a × b) × c
This is known as Associative Law of Multiplication in the Set of Whole Numbers.
For example: 3, 5 and 7 are three Whole Numbers then
3 × (5 × 7) = 3 × 35
= 105
&
(3 × 5) × 7 = 15 × 7
= 105
Hence, it is established that, 3 × (5 × 7) = (3 × 5) × 7
- d) Existence of Multiplicative Identity: For every Whole Number a, there exist a unique Whole Number 1 (one) such that
a × 1 = 1 × a = a
1 (one) is called the Multiplicative Identity in the Set of Whole Numbers
For example: 5 is a Whole Number, then
5 × 1 = 5
&
1 × 5 = 5
Hence, it is established that, 5 × 1 = 1 × 5 = 5
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Fast Facts:
- The Set of Whole Numbers is not closed with respect to the operation of Subtraction. The Difference of two Whole numbers is not always a Whole Number.
Illustrate yourself with suitable example.
- The Set of Whole Numbers is not closed with respect to the operation of Division. The Quotient of two Whole numbers is not always a Whole Number.
Illustrate yourself with suitable example.
