We look at how stacks can be added by removing the overload that often appears when one stack is placed on top of another stack.
The stack can be added concretely through a principle of internal trade where a full stack of 10 1s is traded with one 10-bundle.
And the result can be predicted by a calculation on paper using either a vertical way of writing the stacks using carrying to symbolise the internal trade; or using a horizontal way of writing the stacks using the FOIL principle.
In both cases the overload can be recounted by the recount-equation T=(T/b)*b or transferred by the restack-equation T=(T-b)+b.
Q: How to add stacks concretely?
A: T=27+16= 2ten7+1ten6= 3ten13=?
Q: How to add stacks abstractly?
A: By restacking overloads predicted by the restack-equation T= (T-b)+b
T = 27+16 = 2 ten 7+1 ten 6 = 3 ten 13 = 3 ten 1 ten 3 = 4 ten 3 = 43
Vertical calculation uses carrying. Horizontal calculation uses FOIL