The usage of 'majority'

Both of the following sentences are correct:

1. A majority of students recognize the importance of the issue.

2.The majority of students recognize the importance of the issue.

'A majority' would refer to a number that you could name, the number that makes the difference. For example:

The majority of the people (64%)voted for Blake.

Both 'a majority of' and 'the majority of' can mean 'most of' or 'the greater number of.'

In the first example, 'a majority of 100 votes' means 100 votes more than his opponent. If Blake's opponent received 200 votes, then Blake received 300 votes. If Blake's opponent received 2,000 votes, then Blake received 2,100 votes.

Just 'a majority' means,  'most of.' But, 'a majority of xx' refers to the gap between the lower number and the higher number.

For example:

A/The majority of voters voted for John Smith.

But:

John Smith won by a huge majority/ a majority of 23,000 votes.

As to the more details about majority,please read this article:MAJORITY.doc （文件大小：69.50 KB）