In mathematical computation, commutative property or commutative law explains that order of terms doesnâ€™t matters while performing an operation.Â Although the official use of this law began at the end of the 18th century, it was known even in the ancient era. This property is applicable only for two operations: addition and multiplication. Suppose two numbers A and B on addition gives a sum C, then if we interchange the position of A and B, the result will be C only, such as;Â A + B = B + A = C.Â Â For example, 4 + 3 = 7 = 3 + 4; here, whether 3 come before or after the plus sign, the sum of 4 and 3 will be always 7 irrespective of their order. Apart from commutative, there are two more major properties addition and multiplication of integers, they are associative and distributive. Let us discuss all the three properties or laws here.
What is Commutative, Associative and Distributive Property?
There are three major properties used in the mathematical or arithmetic operations followed by integers. They are:
 Commutative Law
 Associative Law
 Distributive Law
Let us discuss all the three laws or properties here.
What is Commutative Law?
The word, Commutative, originated from the French word ‘commute or commuter’ means to switch or move around combined with the suffix ‘ative’ means ‘tend to’. Therefore, the literal meaning of the word is tending to switch or move around.Â It states that if we swipe the positions of the integers, the result will remain the same.
Commutative Property of Addition and Multiplication
According to this property, whether we add or multiply numbers, the answer will remain unchanged even if the position of the numbers are changed. Let A and B are two integers, then;
Hence,

AssociativeÂ LawÂ of Addition and Multiplication
According to the associative law, regardless of how the numbers are grouped, you can add or multiply them. In other words, the placement of parentheses does not matter when it comes to adding or multiplying.
Hence,

Distributive Law of Multiplication
The distributive property of Multiplication states that multiplying a sum by a number is the same as multiplying each addend by the value and adding the products then.
According to the Distributive Property, if a, b, c are real numbers:
a x (b + c) = (a x b) + (a x c)
NonCommutative Law
Some operations are noncommutative. By noncommutative, we mean the switching of the order will give different results. The mathematical operations, subtraction and division are the two noncommutative operations. Unlike addition, in subtraction switching of orders of terms results in different answers.
Example: 4 – 3 = 1 but 3 – 4 = 1Â which are two different integers.
Also, division does not follow the commutative law. That is,
6 Ã· 2Â = 3
2 Ã· 6Â = 1/3
Hence, 6 Ã· 2 â‰ Â 2 Ã· 6
Important Note: Commutative property works for addition and multiplication only but not for subtraction and division.
Examples
Example 1: Which of the following follows commutative law?
 3Â Ã—Â 12
 4 + 20
 36 Ã· 6
 36 – 6
 3Â Ã—~4
Solution: Options 1, 2 and 5 follow the commutative law
Explanation:
 3 Ã— 12 = 36 and
Â Â Â Â 12 x 3 = 36
=> 3 x 12 = 12 x 3 (commutative)
 4 + 20 = 24 and
Â Â Â Â Â 20 + 4 = 24
Â Â Â Â Â => 4 + 20 = 20 + 4 (commutative)
 36 Ã· 6 = 6 and
Â Â Â Â Â 6 Ã· 36 = 0.17
=> 36 Ã· 6 â‰ 6 Ã· 36Â (non commutative)
 36 âˆ’ 6 = 30 andÂ
Â Â Â Â Â Â 6 – 36 = – 30
=> 36 – 6 â‰ 6 – 36Â (non commutative)
 âˆ’3 Ã— 4 = 12 and
Â Â Â Â Â Â Â 4 x 3 = 12
=> âˆ’3 Ã— 4 = 4 x 3Â (commutative)
To solve more problems on properties of math, download Byju’s – The Learning App from Google Play Store and watch interactive videos.