I just started learning Japanese for a few months, and I saw a sentence recently:
留学生はアジア人が多く、その他は3割です。
I feel strange that the sentence uses 多く instead of 多い. 多く is an adverb, 多い is an adjective. The word before 多く is アジア人, which is a noun, shouldn't I use the adjective 多い to modify the noun? What's the underlying rule here?
Let's look at your sample sentence.
留学生はアジア人が多く、その他は3割です。
You have two independent clauses here. To join independent clauses in a sentence, you need to use a conjunction. Japanese verbs and adjectives have a special conjugation form sometimes called the "conjunctive", also known more informally in English as the "-te form".
If we were to use the -te form in your sample sentence, we would have:
留学生はアジア人が多く[て]{●}、その他は3割です。
But we don't have that.
This is because it is also possible to use the so-called "adverbial form" or "infinitive form" or (for verbs) the "-masu stem form", without the -te suffix, as a conjunction.
If we were to use this shorter form to conjoin the two clauses in your sample sentence, we would have:
留学生はアジア人が多く、その他は3割です。
In your question, you ask more specifically, "why can't we use 多い【おおい】 here?" This is because you cannot use the regular form of an adjective (or verb) to conjoin clauses. If we just said:
留学生はアジア人が多い、その他は3割です。
... it wouldn't be grammatical.
It's a bit like why you have to use "and" in English in sentences like "There are a lot of Asians among exchange students, and other ethnicities comprise only 30% of the total." In Japanese, instead of a separate conjunction word like "and", we conjugate the verb or adjective that finalizes the first clause into the adverbial / infinitive (or, in Japanese, the 連用形【れんようけい】), or into the -te form.
