the number of sth 做主语谓语动词用单数还是复数还有number of 作主语呢

the number of 是......的数量的意思，谓语动词必须接单数。
如：The number of the students in our school is 235.
a number of 是许多的意思，相当于a lot of.谓语动词用复数。
如：A number of people were injured in the terrible earthquake.

the number of+名词作主语，谓语动词用单数
A number of + 名词作主语，谓语动词用复数

主语是“ a number of+ 复数名词”时，谓语动词要用复数形式；若主语是“ the number of+ 名词”时，谓语动词则要用单数形式。例如：
The number of the people invited was fifty, but a number of them were absent for different reasons.

都用单数

此词组的意思是某物的数量，用单数！

绝对是接复数
Eg: The birth rate is the number of births compared to the number of the people.
The number of cases of assault or the number of assault on policemen is increasing.

the number of+名词作主语,谓语动词用单数.
而A number of + 名词作主语,谓语动词用复数.

the number of+复数名词作主语，意思是“。。。。。的数量，数目”， 谓语动词用单数。
而A number of +复数 名词作主语，意思是“许多。。。。。。”， 谓语动词用复数。