
Steps  28 + 165  
1.  Equate the digits of both the numbers by prefixing imaginary Zeroes in front, and separate the columns for each place.  In this case, 0  2  8 + 1  6  5  

2.  Sum the digits of each column, even if the the result is aśūddha (impure, to mean more than one digit holding a position).  In this case, 0  2  8 + 1  6  5  1  8  13 

3.  Conduct a śūddhikaran to purify the number, so that every place is held by only one positive digit.  In this case, [1,8,13] has 13 in the One's place. So, only 3 can remain, and the 1 needs to be added to the next column, containing 8. Thus, [1,8,13] = 193, which is the answer! 
2  3  4 4  0  3 5  6  4 + 7  2  1  18  11  12 By śūddhikaran, [18,11,12] = 1922 Thus, 234 + 403 + 564 + 721 = 1922 
7  8  9  2  4 2  7  2  7  2 + 7  2  6  8  4  17  ^{1}8  ^{1}8  ^{1}8  ^{1}0 Thus, 78924 + 27272 + 72684 = 178880 Note that, the 'carryover' digit is taken into consideration for each columns. 

Steps  34  18  
1.  Equate the digits of both the numbers by prefixing imaginary Zeroes in front, and separate the columns for each place.  In this case, 3  4  1  8  

2.  Convert the digits as Rekhanks, and sum the digits of each column, even if the the result is aśūddha (impure, to mean more than one digit holding a position)  In this case, 3  4 + 1  8  2  4 

3.  Conduct a śūddhikaran to purify the number, so that every place is held by only one positive digit.  In this case, [2,4] has 4 in the One's place. So, 1 needs to be taken from the previous digit and given to the next digit, which becomes (10 + 4) = (10  4) = 6. Thus, [2,4] = 16, which is the answer! 
5  1  2  4 + 3  6  0  8  2  5  2  4 By śūddhikaran, [2,5,2,4] = 1516 Thus, 5124  3608 = 1516 
7  8  9  2  4 + 2  7  2  7  2  5  1  6  ^{1}5  2 Thus, 78924  27272 = 51652 Note that, the 'carryover' digit is taken into consideration for each columns. Also, for negative results, it is replaced with the relative complement from the nearest m × 10 and m is carriedover, for consideration in next column. For example above, 2 + 7 = 5 and, 10 + 5 = 5. Hence, carryover of 1. 
7  3  8  1 + 0  2  3  4  7  1  4  ^{1}7 Thus, 234  7381 = (7381  234) = 7147 

6  3  7  1 2  6  4  7 8  0  9  6 7  3  8  1 + 1  2  3  4  5  ^{1}6  7  3 Thus, 6371  2647 + 8096  7381 + 1234 = 5673 
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