If you want some up-to-date (and very in-depth) information on ancient Mesopotamian arithmetic, you might be interested in the paper "Floating Calculation in Mesopotamia" [1]. By "floating" the author means what I would call floating-point. If I understand the paper correctly, there were actually two base-60 systems: one for counting (addition and subtraction) and a different one for multiplying and dividing.

[1] http://cdli.ucla.edu/pubs/cdlp/cdlp0005_20160501.pdf