Ok, I see where the problem is coming from.
This problem arises from using ppm as our units for measurement. Technically, ppm is 1 thing per million total things, which we transform into grams per million grams and eventually mg per liter for concentrations in water. While this is a practical measurement for certain applications, it fails in many others. The comes down to its dependence on the mass of what you're looking at. For comparison between chemicals, you need to use moles (the unit, not the rodent), which actually counts number of molecules rather than mass in solution. The issue is that 1 mole of nitrite weighs about 3.3x as much as one mole of ammonia, and nitrate weighs about 4.5x as much one mole of nitrate. This is due to the additional oxygens attached to the nitrogen.
Concept in action: you dose your aquarium with 4 ppm of ammonia. Over the coming weeks, the bacteria will convert it into a total of about 12 ppm nitrite and 18 ppm nitrate (but not all at once, obviously). If we were using moles, we would dose, say, 1 mmol of ammonia (or whatever it converts into, I'm not going to do unit conversions on vacation), which would turn into 1 mmol of nitrite and then 1 mmol of nitrate.
What does that mean to us? If you are going to compare nitrate levels to nitrite levels, or any two measurements using ppm, you need to keep in mind that these units are NOT equivalent. If you wanted to calculation total nitrogen, you would have to multiple each ppm by the total contribution that nitrogen makes to each component. That being said, there's really no benefit in doing that as it doesn't really give you a meaningful number. We spend that vast majority of our time comparing two measurements of the same unit, ie, ppm nitrate vs ppm nitrate, ppm ammonia vs ppm ammonia, etc. Dividing by 4.4 will give you total nitrate nitrogen concentration rather than nitrate concentration, but that doesn't really tell you anything that nitrate concentration wouldn't already tell us.
Any questions in this?
Edit disclaimer: most numbers were largely estimated because I haven't had my coffee yet. If anyone would like, I can get some more meaningful numbers in here.