would like to know which one is correct:

many more or much more

thanks in advance
Depending on what you quantify, both are correct.

1. Use many and few for countable nouns.

I have many/few friends.
There are many more opportunities waiting for you.

2. Use much and little for uncountable nouns.

She has much/little money in the bank.
There is much more pollution in the city.

3. Use "a lot of" and "lots of" for both countable and uncountable nouns. Use "is/was" for uncountable and "are/were" for countable nouns.

I have lots of things to do today.
You'll be in lot of trouble if you get caught.
There is a lot of crime in Manhattan.
There are a lot of cars on the road at this hour.
There is a lot more pollution in the city than in the country.
There are a lot more people now than last week.
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I think the second one is true.

And one more question.

when do we use "much more"?
Students: We have free audio pronunciation exercises.
 Teacher Eric's reply was promoted to an answer.
There are many more people who live in China than people who live in Hawaii.
There is much more milk in this glass than in that cup.

Both are correct. Emotion: smile
both of them can be used before countable nouns,but before uncountable nouns ,we must use much more
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hey ...can i say ...

travel by bus is much more cheaper....
Anonymoushey ...can i say ...
travel by bus is much more cheaper..
No. The ending -er on cheap already means more, so you can't have both more and -er. (And don't forget to capitalize the first word of every sentence.)

Travel by bus is much cheaper.

In my grammar lesson http://englishfather.com/nouns I learnt that 'much' is used in case of uncountable noun & 'more' is used in case of countable noun. I read some sentences with "much more". Can you explain it with some instances.
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I followed that link and found nothing like that.
Anonymousnouns I learnt that 'much' is used in case of uncountable noun & 'more' is used in case of countable noun.
That information is not correct as it stands.

In any case, if you read through the posts in this thread, you should find the answer to your question
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