We look at how we add per-numbers by transforming them to totals.
The $/day-number a is multiplied with the day-number b before added to the total $-number T:
T2 = T1 + a*b. 2days @ 6$/day + 3days @ 8$/day = 5days @ 7.2$/day.
And 1/2 of 2 cans + 2/3 of 3 cans = 3 of 5 cans = 3/5 of 5 cans.
Repeated and reversed addition of per-numbers leads to integration and differentiation:
T2 = T1+a*b; T2-T1 = +a*b; DT = ∑a*b = ∫y*dx and
T2 = T1+a*b; a = (T2-T1)/b = DT/b = dy/dx
Q: What is a prime number?
A: Fold-numbers can be folded: 10=2fold5. Prime-numbers cannot: 5=1fold5
Q: What is a per-number?
A: Per-numbers occur when counting, when pricing and when splitting.
Q: How to add per-numbers?
A: The $/day-number a is multiplied with the day-number b before added to the total $-number T: T2 = T1 + a*b