Re: problem with the word "number" plurial or singular (there are a large number of..
1. The number of visitors to the website has decreased.
2. A number of visitors to the website have complained about its controversial content.
It depends on the meaning of the sentence.
In #1, for example, it is the number that has "decreased". The underlined part simply qualifies "number". So the verb is singular.
In #2, on the other hand, it is the visitors who have "complained". The underlined part simply qualifies (pre-modifies) "visitors". So the verb is plural.
Let me know if it's still puzzling!
Not a professional ESL teacher.