Number Properties - Definition with Examples

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Number Properties

The four main number properties are:

 

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

Commutative property

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

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

Associative Property

( 4 x 7 ) x 5 = ( 4 x 5 ) x 7 =150

 

Identity Property:

Additive identity Multiplicative identity

Additive identity is a number, which when added to any number, gives the sum as the number itself.

This means, the additive identity is “0” as adding 0 to any number, gives the sum as the number itself.

Additive identity

Multiplicative identity is a number, which when multiplied by any number, gives the product as the number itself.

This means, the multiplicative identity is “1” as multiplying any number by 1, gives the product as the number itself.

Multiplicative identity

 

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:

Distributive Property

 

Example of distributive property using addition

Example of distributive property using subtraction

Distributive property using addition Distributive property using subtraction

 

  Fun Facts

  • The additive identity property is also called the zero property of addition.

  • The commutative property gets its name from the word commutes, meaning move around.

 

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