It has to do with an old habit of counting by twenties instead of tens. 30 used to vingt-et-dix, 40 deux-vingt, etc. Trente, quarante, cinquante and soixante replaced it gradually, but it stayed with 70, 80 and 90.
Though outside France, French speakers use septante and nonante. In Switzerland, they say octante or huitante instead of quatre-vingt.
Danish has a similar system for numbers above 50; not only do they call 60 and 80 by names that would expand and clean up [1] and translate as "three-twenties" and "four-twenties", but 50 is called "half-three-twenties", 70 is "half-four-twenties" and 90 is even "half-five-twenties" (although they don't call 100 "five-twenties" anymore).
[1] Expand and clean up because, being Danish, the words are horribly slurred together into a kind of linguistic sludge.
Yes, and so do the Scandinavian languages: snes. But this word is not used in the slurry that becomes the Danish "treds" and "firs" and "halvfems", said slurry is actually derived from longer phrases that include and end with the word for "twenties".
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