You don't generally have to do any long division, because there are only a few ranges of speed you need to deal with. Dwarves and small characters move at 20', medium characters and dwarvish or small barbarians at 30', medium barbarians, ponies, and wardogs at 40', and horses at 50'. Encumbered/armored speeds (with more than light armor) are 15', 20', 30', and 35'. Read and learn, and you're done.
Dwarvish barbarians have a base move of 30'; like other characters with a base move of 30', they have a move of 20' when encumbered. (With heavy encumbrance or armor, they lose their barbaric speed bonus, and crawl along at 15' like the other encumbered dwarves.)
Monks would be a pain, but fortunately, they lose all of their bonus speed when encumbered or armored. Whew!