SOME  RULES OF ADDITION OF INTEGERS –

1) The sum of two integers is always is an Integers. If x & y are an Integers then the sum of both Integers (x + y) is always is an Integers.

2) For all Integers x & y, (x + y) = (y + x)    [ Communicative Law ]

3) For all Integers x,y & z, we consider (x + y) + z = x + (y + z)  [ Associative Law ]

4) The Integers ‘0’ zero is the additive identity in Integers, as ;  x + 0 = 0 + x = x

5) For every Integers  (+ x) + (- x) = (- x) + (+x ) = 0   [ Existence of Additive Inverse ]

a) The sum of two positive integers is a positive integer which have been obtained by taking sum of the numerical values of the addends.

b) The sum of two negative integers is obtained by giving the negative sign to the sum of their numerical values.

c) To add positive and negative integers, we find the difference between their numerical values and give the sign of integers with more numerical values.

Example.1)  (+23) + (+31) = ?

Ans.)   (+23) + (+31) =  + ( 23+31) = + 54      (Ans.)

Example.2)  (-12) + (-25) = ?

Ans.)   (-12) + (-25) = - ( 12 + 25) =  - 37     (Ans.)

Example.3)    ( -25 ) + (+10)

Ans.)  ( -25 ) + (+10) =  (-25 + 10) =  -15 (Ans.)