My learning of math addition

Here are some good way's that help me with my math's.
  
1 2 3 4 7 8 3 1 + 4 5 6 2 1 3 3 2 =?

This is how I would work it out. 
                          1
           1 2 3 4 7 8 3 1     1 +2 =3 
           4 5 6 2 1 3 3 2     3 +3=6                                           5 7 9 6 9 1 6 3

 you would plus the 2 numbers one on the top and one on the bottom. If you came up to one that made more than 10 Example   9 + 1 =  11  so you would take the one  and put the other one and put it to the next number making it go to the number over it. Example  5 then the one put to it makes 6.