Usage of 都, 都不, 不都

都, which basically means all, is an adverb that shows up in our daily talk with very high frequency. It is very unique that 都 can only refer to plural things which precede it, and has the effect of 'totaling' the plural or collective noun.

陈述句 Declarative sentence

In English, there are 'both and all' to describe two or more subjects having the same feature or do the same action. 都 covers 'both' and 'all'. 
For example,
I am a teacher.               -->  我是老师。
You are a teacher.         -->  你是 老师。
(There are two teachers now.)
We are both teachers.     -->  我们都是老师。
He is also a teacher.        -->  他也是老师。
(There are more than two teachers now.)
We are all teachers.        -->  我们都是老师。

否定句 Negative sentence

There are two different negative sentences.

'both not' and 'all not' negative sentence

For example,

I am not a teacher.         -->  我不是老师。

You are not a teacher.    -->  你不是老师。

(Two people both are not teachers.)

Both of us are not teachers.      -->  我们都不是老师。

He is not a teacher either.                 -->  他也不是老师。

(More than two people are not teachers.)

All of us are not teachers. / None of us are teachers.   -->  我们都不是老师。

'not both' and 'not all' negative sentence

For example,
I am not a teacher.             -->  我不是老师。
You are a teacher.              -->  你是老师。
Not both of us are teachers.    -->   我们不都是老师。
He is a teacher.                   --> 他是老师。
Not all of us are teachers.   -->   我们不都是老师。

Now it's your turn. Please translate one of the following sentences into Chinese and type as your comment to get feedback from me.

1. We both eat breakfast.
2. They all want to go.
3. None of them wants to go.
4. Neither of his parents likes hiking.
5. The apple is expensive. The pear is not expensive. Not all the fruit is expensive.