Translation:One out of ten Slovaks live in Czechia.
Both "one out of ten" and "one in ten" work equally well on the English side.
However, I would expect the verb to be "lives," in agreement with "one," which is essentially the subject of the sentence. But when I ran "One out of ten boys are tall" through several online grammar checkers, I was surprised to find that only a few changed "are" to "is." Curious.
The translation "One in ten Slovaks live in Czechia" should be accepted. "In ten" is correct (it need not be "of ten" or "out of ten"), and it represents a plural figure, as there are far more than just 10 Slovaks in the world. https://en.oxforddictionaries.com/grammar/matching-subjects-and-verbs
Pretty confusing when he is one, isn't it. Similar as a lot, it is a lot, so one lot and still you have plural in English, weird.
What I wanted to say, they present it as obvious in that link that it is plural that they are members, but it is not obvious at all, it is a feature of English that must be learned and remembered. Other languages, Czech among them, use singular in the same situations.
Also, it is not a strict dogma, cases of singular use do exist:
Plural concord is predominant with expressions of the type one in / out of numeral, though singular verb forms are also found:
[One in] five were scared of other prisoners, (news)
[One in] five pairs of socks sold in Britain is made by Sherwood. (news|)
In these expressions the reference is to a group. Singular concord is presumably sometimes chosen because of the strong pull of one in the direction of the singular (cf. the one of constructions taken up in 3.9.3).
Longman Grammar Of Spoken And Written English By Samy Salah
So, changed to plural, but singular will remain accepted.