> "Nine times" literally means multiplied by nine

Rather, "nine times larger" means multiplied by nine, and "nine times smaller" means divided by nine. This is basic and not particularly awkward, certainly not more so than e.g. positive/negative correlation, or many much more awkward and more common linguistic constructions, IMO.

If you have to edit out words (i.e. context) to argue a phrase doesn't make sense... I am not sure what mental model you have for natural language, exactly, but it certainly isn't a very robust one.