"Divide by three" is the only way I know to say this but I'm looking for a single word, if one exists.
The OED defines third, verb, as such:
To divide (anything) into three equal parts; to reduce to one third of the number or bulk.
and it gives an example from 1874:
Such a course would have halved or thirded the number of our subscribers.
However, as choster pointed out in a comment, this seems to be rare.
I did an ngrams search which shows the relative changes in halved, thirded over time, and the usage of halved has increased while the usage of thirded has decreased. Similarly, the usage of thrice is also decreasing over time. This suggests to me that you should avoid using the word "thirded" despite it being a recognized usage.
Another answer provides the word "trisect". This word doesn't fit precisely in the collection "quartered, X, halved", but rather goes with "bisect, trisect, quadrisect". These words seem to me to be more technical in nature, used for geometry (e.g. Trisecting the Angle) or other mathematical or scientific contexts. Also, trisect can only be used for the sense "to cut into three equal parts" and not in the sense "to reduce to one third the size".
- If you want to fill the "quartered, halved, etc" group, use thirded.
- If you want language people actually use, just say "cut into thirds" or "divided into three" or something similar.
- If you need a current, single word, trisected is probably your best bet but it doesn't really fit the pattern nor satisfy all the meanings.
- to divide into three usually equal parts.
Halve means two things:
- to divide (something) into two equal parts: to divide (something) into halves
- to reduce (something) to one half of the original amount or size
For the first, trisect is a good option, but in my experience the second meaning is more common, as in The budget for our project was halved.
You cannot equally say: *The budget for our project was trisected, as that sounds as if it was split into three, and shared among three parties.
Your best bet for the second meaning is probably: The budget for our project was reduced to a third.
(Actually, trisect already sounds a bit mathematical and formal; it doesn't sound like something you'd say in casual conversation. Split in three is better there.)
I don't think there is a long-standing English word for dividing into three parts. Also, it looks like halve is from a word that originally meant divide without carrying the specific meaning of divide in two:
I would also note that neither halve nor half appears to bear any relationship to words for two or three. By contrast twice and thrice are words for two and three with endings that signify use as an adverb.