Calculus

Calculus adds per-numbers by areas.

Adding 3 kg at 4 $/kg and 5 kg at 6 $/kg, the unit-numbers 3 and 5 are added as 3+5, and the per-numbers 4 and 6 are added as 3*4+5*6, i.e. as the area under the per-number graph, i.e. as integration combining * and +.

As reversed integration, differentiation produces per-numbers by combining — and /.