Lattice addition is probably one of the most difficult to understand algorithms. Not only is it typically confusing for people, it is difficult to understand why this works.

When drawing the diagonal lines, we are essentially breaking up the result into two pieces: the piece that has the same place value as the numbers we are adding, and the piece that has a larger place value than the numbers we are adding.

The diagonal pieces that need to be added will consist of two parts, and they will each have the same place value. In our example, adding 4 and 8 gives us 2 ones, and then 1 ten. Adding 8 and 3 gives us 1 ten and 1 hundred. So when we add along the second diagonal, we have 1 ten (that was regrouped from the ones place) and 1 ten (that came from adding the tens) to get a total of 2 tens. Essentially, the part above the diagonal line is the part that you need to “carry” or regroup.