Number Properties - Definition with Examples

Number Properties

The four main number properties are:

• Commutative Property

• Associative Property

• Identity Property

• Distributive Property

Commutative property: 

The commutative property states that the numbers on which we perform the operation can be moved or swapped from their position without making any difference to the answer.  

This property holds true for addition and multiplication, but not for subtraction and division.

Example of the commutative property of addition

 3 + 5 = 5 + 3 = 8

Hence, the commutative property of addition for any two real numbers a and b is:

                a + b = b + a

Example of the commutative property of multiplication

Hence, the commutative property of multiplication for any two real numbers a and b is:

                a x b = b x a

We can also say that in commutative property, the numbers can be added or multiplied to each other in any order without changing the answer. 

Associative Property:

The associative property gets its name from the word “Associate” and it refers to the grouping of numbers. This property states that when three or more numbers are added (or multiplied), the sum(or product) is the same regardless of the grouping of the addends (or multiplicands). 

For example:

 (3 + 4) + 5 = (4 + 5) + 3

( 4 x 7 ) x 5 = ( 4 x 5 ) x 7 =140

Identity Property:

Distributive Property:

Distributive property helps us to simplify the multiplication of a number by a sum or difference. As the name suggests, it distributes the expression.

For example:  a x (b + c)

Using distributive property, we can expand the expression as:

Example of distributive property using addition	Example of distributive property using subtraction