# Properties of Multiplication

There are few properties of multiplication which makes the calculation of multiplication easier and less time consuming. Moreover, by using the properties of multiplication we can easily find the product of large numbers.

Commutative Property of Multiplication:

This property states that whatever is the order of the multiplicand and the multiplier the product is always the same. That is:

Examples on Commutative Property of Multiplication:

2 × 3 = 3 × 2 = 6

52 × 2 = 2 × 52 = 104

Closure Property of Multiplication:

This property states that if p and q is a whole number then the product of p and q will also be a whole number. This is shown with the help of few examples:

Examples on Closure Property of Multiplication:

7 × 8 = 56

Where 7 and 8 are whole numbers and the product 56 is also a whole number

11 × 5 = 55

Where 11 and 5 are whole numbers and the product 55 is also a whole number

19 × 2 = 38

Where 19 and 2 are whole numbers hence the product 38 is also a whole number

Multiplicative Identity Property of Multiplication:

This property states that if any whole number is multiplied by 1 then the product is the whole number itself. Hence 1 is the multiplicative identity as the value of the whole number does not change.

Examples on Multiplicative Identity Property of Multiplication:

5 × 1 = 5

89 × 1 = 89

150 × 1 = 150

Multiplication with Zero Property:

This property states that if any number is multiplied with zero then the product of multiplication is zero only.

Examples on Multiplication with Zero Property:

0 × 5 = 0

0 × 90 = 0

0 × 560 = 0

Distributive Property of Multiplication Over Addition:

This property states that if the multiplicand is expanded into two or three addends and then each addend are multiplied. The product of each of them is then added to get the final answer.

Examples on Distributive Property of Multiplication Over Addition:

·         6 × 5 = 30

Or, 5 × (3 + 3) = 30

Or, 5 × 3 + 5 × 3 = 15 + 15 =30

·     17 × 3 = 51

Or, 3 × (10 + 7) = 51

Or, 3 × 10 + 3 × 7 = 30 + 21 = 51

·     23 × 6 = 138

Or, 6 × (20 + 3) = 138

Or, 6 × 20 + 6 × 3 = 120 + 18 = 138

In these examples we can see that the product remained unchanged ny applying the associative property of multiplication.

Associative Property of Multiplication:

This property states that if p, q, r are the three whole numbers then by changing the arrangement of the whole numbers the product of the numbers does not change.

Examples on Associative Property of Multiplication:

(i) (5 × 6) × 2 = 5 × (6 × 2)

Þ 30 × 2 = 5 × 12

Þ 60 = 60

(ii) 7 × (3 × 2) = (7 × 3) × 2

Þ 7 × 6 = 21 × 2

Þ 42 = 42

Therefore in both the examples it is seen that by changing the arrangement of the whole numbers their product remained unchanged.

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