I'm familiar with the concept of how たくさん、多く、and 多い are used in relation to
nouns (多くの人、人が多い、etc.) but I'm still unfamiliar with how you can say the
expression "a lot of [verb]". I know, for example, たくさん食べる means "a lot of
eating," but I'm unsure if you need to distinguish 多く and 多い when it comes to
verbs.

In addition, here's what I know; tell me if I got anything wrong.

多く and 多い can carry an additional meaning of "too much." たくさん doesn't.

While there's a grammatical distinction between 多く and 多い, たくさん doesn't need
this.

Thanks!
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2015-09-26T23:42:09.677
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word-choice
たくさん vs. 多く vs. 多い when used on verbs?
First of all, I apologize for posting this as an answer, since I still don't
have enough reputation to post it as comment.

I might be forgetting something but from what I remember, たくさん is more about
intensity (but can also be about quantity depending on the context), while 多い
and 多く are more about quantity.

[this answer might provide a better
explanation](https://japanese.stackexchange.com/a/881/7668)
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At first, basic concept about some words which you posted is below.

  1. "多く" and "たくさん" are adverbs, and these words are same meaning.
  2. "多い" is adjective.

Based on these, I share you some example sentences below.

  1. (多く)たくさん + 食べる [adverb + verb]
  2. (多く)たくさん + 飲む [adverb + verb]
  3. 車が + 多い [subject + adjective]
  4. 人が + 多い [subject + adjective]

Hope it helps.
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2015-09-27T10:51:14.573
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In addition to htcoelho's link, I'd like to point out that たくさん doesn't mean
something is common, I mean, for example, you can say 多くの人はスマートフォンを使っている for
"many people use smartphones" meaning that use of smartphones is common. But
you can't say たくさんの人は… in that meaning. (If it meant "a person who has a lot
of something uses a smartphone", it would be fine.)

(Though this is complicated and may be confusing) That said, when you
reconstruct it through spectrum of neutral description, you can say
たくさんの人が…使っている. Being common is now regarded as largeness of amount in a moment
that's cut out by observation. In addition, you can say こんにちでは、たくさんの人が…, for
some reason.

Edit: たくさん can mean "too much" too. e.g. もう たくさんだ！ It's enough!
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