Addition:Vedic Mathematics does not have techniques to help with
addition unlike multiplication, division or factorisation, though it provides
some interesting checking methods. 

Vedic Mathematics does not talk about simplified addition. However it does
provide an interesting way of checking the result for any addition via
technique called the ??Digit Sums Check??. To understand this technique please
view the following movie:

Now using the Digit Sums Check please try to check if the answers for the
following additions are correct:

  3456  --> 3+4+5+6 = 18 --> 1+8 = 9 
+ 7687  --> 7+6+8+7 = 28 --> 2+8 = 10 --> 1
_______
  11143 --> 1+1+1+4+3 = 10 --> 1 i.e. 9+1 = 10 --> 1

So sum is correct. Note this technique is not full proof in the sense that if
someone wrote the answer as 18343 the sum of digits would come equal to 1. But
this is not the correct answer. However the method can be used for a quick
second check of the result. Also small careless mistakes can be easily
detected by this method. 

Try some more checks:

1)  3455			2)	75668		           3) 867777						
   +6475		             +   6576		       	    + 898989
   ______	                       _______		            ________
    9940			  	82244		             1766766	


Answers: 1 is incorrect and 2 and 3 are correct.

If you are as impatient as me and you honestly tried solving the problems
above, you would be saying well the checking is so cumbersome that I need to
check the check result!!! Well Vedic Maths is all about simplicity. So
obviously the Check Digits is not complete without discussing the "Casting Out
of Nines" method. Please take a look at the movie below to appreciate this
technique.

Now try the same problems that we had struggled with earlier:

  3456  --> 3+4+5+6 --> 9 
+ 7687  --> 7+6+8+7 = 7+2+8+1+7+2+1 --> 1  (Note to make 9s I split the number 6 to 2+1+2+1. With little practice you can do this mentally)
_______
  11143  --> 1+1+1+4+2+1 --> 1 i.e. 9+1 = 10 --> 1

Now retry the following examples:

1)  3455			2)	75668	                  3)  867777						
   +6475			     +   6576                       + 898989
   ______		                _______                     ________
    9940			 	82244			     1766766	

Does it simplify things? 

Take a break now and let your brain sub-conciously absorb what you have read
till now. It has been found that long term memory is increased if you read
stuff with a gap, i.e you read something and then come back to the same topic
again after some time then your retention of the concept is for a longer term.

Hope you had an interesting break!! Please try to recollect all that you had
read in the earlier sections...The Digit Sum Check, the Casting out of nines
technique. Now try to check some more addition examples.

1)  96789			2)      78668                    3)     67777						
   +45621			     +  86576			    + 98989
   ______		              _______		             ________
   142410			       165244			     165766

4)  9622			5)      23567	                  6)     87393						
   +6475			     +  12332			    + 12238
   ______		               _______		             ________
   16097 			 	37899			      99631

7)  88992			8)      46804	                  9)  2468						
   +12344			     +  23676                         + 2009
   ______                              _______		           ________
   101336			 	70483			      4479

 
Did you get the wrong answers. Would it have helped if you had this problem in
the office or in the school to quickly check the results of your calculation.

Wrong Answers in the above cases: 3, 5, 8, 9