> In basic middle school math it’s common to multiply different units as a basic conversion mechanism EDIT: Yes, you multiply the units `2m * 2s` : you first m

> In basic middle school math it’s common to multiply different units as a basic conversion mechanism EDIT: Yes, you multiply the units `2m * 2s` : you first multiply the units to get: `m.s`. This is what I say: you convert everything to the same units before doing the calculations. > Multiplying by the same unit is semantically equivalent to “x times 1 is identity(x)” This is wrong. 1kg * 1kg = 1kg² period. What you're saying is `2kg * 1 = 2kg`, which is right, because `1` is a scalar while `2kg` is a quantity. This is completely different than multiplying 2 quantities. > It would not imply I’m multiplying the units, but rather the scalar value of the unit. That's where you're wrong. When doing arithmetic on quantities, you have 2 equations: x = 2kg * 4s unit(x) = kg * s = kg.s scalar(x) = 2 * 4 = 8 x = 8 kg.s Or x = 5m / 2s x = (5/2) m/s x = 2.5 m/s There is a meaning to units and the operation you do with them. `5m / 2s` is 5 meters in 2 seconds, which is the speed `2.5 m/s`. `2m + 1s` has no meaning, therefore you can't do anything with the scalar values, and the result remains `2m + 1s`, not `3 (m+s)`.