**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:****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.*