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
| Additive identity | Multiplicative identity |
An 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. | A 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. |
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 |
 |  |
| Fun Facts: 1. The additive identity property is also called the zero property of addition. 2. The commutative property gets its name from the word commutes, meaning move around. |