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a number of为量词短语，表示“许多……”，中心词是这个短语所修饰的复数名词，所以作主语时，谓语动词用are。the number of表示“……的数量”，中心词为number，指的是of后边名词的数量，数量是个抽象概念，因此谓语动词用is。
a number of用法1.A number of students of our school have read that magazine.
我们学校有很多学生都看过那本杂志。
2.A number of wild animals have been found in the forest.
森林里发现了很多野生动物。
3.A number of houses were burnt down in the fire .
许多房子被烧毁了。
4.He has left a number of books with me .
他把许多书存放在我这儿。
5.He discovered a number of bright young men .
他发现了一批很有才华的年轻人。
6.There are a number of restaurants in this city.
这个城市有很多餐馆。
the number of用法1.The number of students in our school has grown from 1,000 to more than 1,500.
我们学校学生的数量从1000名增加到1500多名。
2.The number of wild animals has become less and less in recent years.
最近几年里，野生动物的数量逐渐减少。
3.The number of students increased .
学生人数增多。
4.The number of cars stolen in this city last month ran into 60 .
这个城市上月被盗汽车的数目达到60辆。
