Addition, subtraction, multiplication and division are the four fundamental operations in mathematics. These operations follow some fundamental properties. All these basis operations may not follow all the properties altogether but each mathematical operation follows a few properties based on some condition. The commutative property is one of the common fundamental properties. This commutative property is applicable for addition and multiplication operations. The other important fundamental properties are –closure property, distributive property, associative property and identity property. Commutative property denotes that the altering position or order of numbers in any addition or multiplication operation will not change the result. Let’s take an example. As 3+5 gives 8, and 5+3 also gives 8. Here the order of the number (3 and 5) is changed but both the sum gives the same answer. Like that in multiplication also, the change of the order of numbers does not change the end result. But in the operations of subtraction and division the changes of the order or position of the numbers will provide different results. This commutative property is not applicable for subtraction and division. We will know more about commutative property in details here.

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## Definition:

The concept of commutative property is known to people from ancient times and this concept started to be used mostly at the end of 18 the 18th century. The word ‘Commutative’ is derived from French word ‘commuter or commute’ which means move around and added with the suffix ‘-ative’ that means tend to. So, the word ‘commutative’ means tend to move around.Commutative property deals with moving around the numbers. If the change of the order or position of position does not change the end result of a mathematical operation then this mathematical operation is commutative.

## Commutative property of addition:

As per commutative property of addition, the addition of numbers will remain unchanged even when the position of the numbers are altered. Let’s take an example. If M and N are two numbers, then according to the commutative property of addition, the answer of the sum of these two numbers will remain unchanged even if the position of the number is altered. So, according to this,it is true that

M+N=N+M

Now take two real numbers to elaborate this.5 and 7 are two numbers. According to the commutative property

5+7= 7+5

5+7=12

And 7+5=12

So,5+7=7+5=12

Some more examples:

12+14=14+12=26

6+8=8+6=14

30+23=23+30=53

## Commutative property of multiplication:

As per this commutative property of multiplication,if the position of numbers changes the result of the multiplication of two numbers will remain unchanged. Have examples. Suppose C and D are two numbers. As per the commutative property of multiplication

C×D= D×C

3 and 5 are two numbers. According to the commutative property 3 × 5= 5×3

3×5=15

And 5×3= 15

So, 3×5 = 5×3 = 15

Some more examples are

12 × 3 = 3 × 12 = 36

9 × 8 = 9 × 8 = 72

6 × 7 = 7 × 6 = 42

In multiplication Distributive property is also used. This property denotes that when a factor is multiplied by the addition or subtraction of two numbers, it is essential to multiply each of the two numbers by the factor. As, A( C + D) = AC + AD

The commutative property is not applicable for subtraction and division. If the order is the numbers will change the end result of them will be different. Take an example:

The subtraction of 7 – 4 = 3

But, if the order of the numbers change, 4 – 7 = – 3

So, the answers of the subtractions are not the same when the position of the numbers are altered.

The divisions also do not obey the commutative property.

So, here we discussed the Commutative properties. To learn more topics in mathematics download Cuemath app. This app will help you to understand mathematical topics in a better way.