Note on Commutative property

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Commutative property is always seen as an important one since it plays an important role in mathematics. Let me show you the main importance of this topic. At the end if you have any suggestion to make feel free to leave your comments on this.

If a and b are any two integer then a+b = b+a.

In other words, the sum of two integers remains the same even if the order of integers (called addends) is changed.

Verification : In order to verify this property, lets us consider some pair of integers and add them in two different orders. We find that the sum remains the same (integer).

Consider the following :

Integer(a) Integer(b) Sum(a+b) Sum(a+b)

5 7 (5+7)=12 (7+5)=12

[Here we observe that 5 is an integer as well 7 is also another integer and now if we add these two integers then the sum of 5+7=12 is also an integer and again similarly if we interchange in place of 5 if we put 7 and in place of 7 we put 5 then also the sum of both the integers will be same 7+5=12].

5+7 =7+5

Integer(a) Integer(b) Sum(a+b) Sum(a+b)

-5 0 {(-5)+0)}=-5 {0+(-5)}=-5

[Here we observe that -5 is an integer as well 0 is also another integer and now if we add these two integers then the sum of (-5)+0=-5 is also an integer and again similarly if we interchange in place of -5 if we put 0 and in place of 0 we put -5 then also the sum of both the integers will be same 0+(-5)=-5].

(-5)+0 =0+(-5)

Integer(a) Integer(b) Sum(a+b) Sum(a+b)

-5 -7 (-5)+(-7)=-5-7=-12 (-7)+(-5)=-7-5=-12

[Here we observe that -5 is an integer as well -7 is also another integer and now if we add these two integers then the sum of (-5)+(-7)=-12 is also an integer and again similarly if we interchange in place of -5 if we put -7 and in place of -7 we put -5 then also the sum of both the integers will be same (-7)+(-5)=-12].

(-5)+(-7) = (-7)+(-5)

-5-7 = -7-5