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Operation on Integers
Addition : In integers, addition can perform using following rule. 
(i)     When adding integers with like signs (both positive or both negative), add their absolute values, and place the common sign before the sum. 
(ii)     When adding integers of unlike signs, find the difference of their absolute values, and give the result the sign of the integer with the larger absolute value. 
(iii)    When the addition and subtraction signs are placed side by side without any number in between, these two opposite signs give a negative sign. 
Subtraction : Subtraction is reverse operation of addition.

Ex.1    Consider 8 – 5. Actually we have to subtract + 3 from 8. So, we need to find a number which when added to 3 gives 8. 
sol:     The answer 5, i.e., 8 – 3 = 8 + (– 3) = 5 
We can change subtraction to addition by adding the additive inverse of the second number to the first number. In the above example –3 is the additive inverse of +3 and vice versa is also possible.
Ex.2     Find the sum of (– 9) + (+ 4) + (– 6) + (+ 3)
Sol.     We can rearrange the numbers so that the positive integers and the negative integers are grouped together. We have 
(– 9) + (+ 4) + (– 6) + (+ 3) = (– 9) + (– 6) + (+ 4) + (+ 3) = (– 15) + (+ 7) = – 8

Ex.3     Find the value of (30) + (– 23) + (– 63) + (+ 55)
Sol.    (30) + (+ 55) + (– 23) + (– 63) = 85 + (– 86) = – 1 

Ex.4      Subtract (– 4) from (– 10)
Sol.:     (– 10) – (– 4) = (– 10) + (additive inverse of – 4) = –10 + 4 = – 6    

 Ex.5     Subtract (+ 3) from (– 3)
 Sol.:     (– 3) – (+ 3) = (– 3) + (additive inverse of + 3)     = (– 3) + (– 3) = – 6

 

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