It's actually very easy to learn, if a nightmare to calculate in your head:
Semi-, hemi-, and demi- are all prefixes meaning "half," so each time you add one in front of a word you get half of that word (e.g., semiquaver, semicircle, semieducated, etc.).
But to keep from saying semisemisemisemi- whenever we want to take half of a half of a half of a half of something, we rotate between semi-, hemi-, and demi-, in that order (think reverse alphabetical order):
- semisomething
- hemisemisomething
- demihemisemisomething
- semidemihemisemisomething
- etcetera ad nauseum
The rotation almost makes it simple to figure out the math:
- semi = half
- hemisemi = quarter (half of a half)
- demihemisemi = eighth (half of a quarter)
- etc.
So depending on how many of them you have strung together, you take them in groups of three starting from the right, and look at the first letter of the group of three or less that remains at the beginning (left). For example:
- hemisemi demihemisemi demihemisemi something
Each group of three (which start with "d"emi) is an eighth, and the group of two that's left over at the beginning (which starts with "h"emi) is a quarter, so we have a quarter of an eighth of an eighth of something.
Of course, figuring out what that reduces down to involves doing math in your head, and doing math in your head involves... well... doing math in your head. So THAT goes over like a lead balloon, especially because your music teacher expects you to do the math in your head while remembering to FACE the music because All Cows Eat Grass and Every Good Boy Deserves Favor, all of which you must do while playing the written music correctly without missing a beat and without looking at which keys your fingers are on.