In this sentence:
I don't fully understand the meaning of
I have found that
付一半 can mean "pay half", but
一人 confuses me (if it refers to one person, why is that form used instead of
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一人 can be thought of as 'per person' or 'each person'.
This grammatical construction is extremely common in Chinese. I think it's called topical construction (correct me if I am wrong here). Essentially, you have the topic of the sentence (bus/taxi fare) at the start, followed by the subject, verb and the rest of the object.
So let's break it down:
I missed the last bit of your question the first time around. The measure word 个 is omitted. It means the same whether it's in there or not (in this case). However, 一人 in this sense is also used in some set phrases (such as 一人做事一人当 - one is responsible for one's own actions), and in those cases, you cannot use 一个人 in its stead. Fivesheep's answer has enough examples to give you a good idea how often it's used.