# Properties of Whole Numbers

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

1. 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

properties of whole numbers
properties of whole numbers worksheets

properties of whole numbers under multiplication

properties of whole numbers ppt

properties of whole numbers in hindi

activities on properties of whole numbers

properties of whole numbers for class 6 ncert