Number Properties – Definition, Types and Examples

Understanding the Number Properties

To comprehend the various number properties, it is essential to explore each concept in detail and understand how they influence mathematical operations. By examining the properties through examples and applications, one can gain a deeper understanding of their significance in mathematics.

Commutative Property

The commutative property asserts that the order in which numbers are added or multiplied does not change the result. As per this number property, moving the order of a number in either addition or multiplication,  doesn’t change the result.

In addition, this means that changing the order of the addends does not affect the sum, and for multiplication, changing the order of the factors does not alter the product.

Commutative Property of Addition 

According to the commutative property of addition, while adding two numbers, the order of the addends does not affect the sum

Let us take two numbers, 3 and 5.

To add those numbers, we can write it as 3 + 5

or, we can also write its as 5 + 3

In both the cases we get the same answers, or in other words,

3 + 5 = 5 + 3 = 8

Commutative Property of Multiplication

When two numbers are mutiplied, the order in which we multiply doesn’t have any impact on the answer.

For example: The product of 2 and 5 is 10. Similarly, the product of 5 and 2 is also 10.

Hence, 2 × 5 = 5 × 2 = 10

Associative Property

The associative property states that the way in which numbers are grouped or associated  in an addition or multiplication expression does not affect the result.

Associative Property in Addition

When adding three or more numbers, the grouping of the numbers can be changed without altering the sum. 

For example: We can group the numbers 4, 7, and 2 as either  (4 + 7) + 2 or 4 + (7 + 2). In both the ways, we get the same sum, i.e. 13.

Associative Property in Multiplication 

When multiplying three or more numbers, the grouping of the numbers can be changed without affecting the product. 

For example: We can group the numbers 3, 2, and 6 as either  (3 × 2 ) × 6 or 3 × (2 × 6). In both the ways, we get the same product, i.e. 36.

Distributive Property

The distributive property describes the relationship between addition and multiplication. It states that when a number is multiplied by the sum of two other numbers, the result is the same as if the number were multiplied by each of the two numbers separately, and then the products were added together.  The multiplication distributes over addition. 

For example: We can take the numbers 7, 2 and 5

According to the number property, 7 × ( 2 + 5 ) = (7 × 2) + ( 7 × 5) = 49

Identity Property

The identity property refers to the existence of an element in a set that, when combined with another element using a specific operation, leaves the other element unchanged.

Identity Property of Addition 

In addition, when we add 0 to any number, the number remains unchanged, or we get the same number as the sum. 0 is called additive identity.

Let’s add 6 to 0, we get 6 + 0 = 6

Identity Property of Multiplication

In case of multiplication, if we multiply 1 to any number, the product will be the same number. Thus, we call 1 a multiplicative identity.

Let’s multiply 4 and 1, we get 4 × 1 = 4

We can understand number properties better with a chart. Let’s assume a, b and c are three numbers.

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