Usage of に to indicate purpose

Question

I'm trying to understand the use of に as a particle to indicate the purpose of someone moving to another place to do something. For example, lets say that I want to say "I'm going home to eat dinner." Would this be written as:

私はひるごはんを食べますにうちへ行きます.

Or, if I wanted to say "I went to the library to study."

私はべんきょうしますに としょかんへ行きました

Are these correct? And does the particle に always come after the verb indicating what action is taken?

P.S: I checked the other topics relating to this, but none of them really cleared up the question I had. So, I'm sorry for posting something similar!

Answer 1

Your understanding of the meaning of に is basically okay, but you must use the masu-stem (aka pre-masu form, 連用形) of a verb before に. Instead of 食べますに or べんきょうしますに, you have to say 食べに or べんきょうしに.

• 私はひるごはんを食べにうちへ行きます。
• 私は勉強【べんきょう】しに図書館【としょかん】へ行きました。

More generally, ～ます/～です is used near the end of a main clause. See: Use of -です／-ます in the middle of a complex sentence

Answer 2

Like naruto says, when we use the masu form, the part of the verb without masu, is the stem.

Besides, it's also correct to say「私はべんきょうにとしょかんへ行きました。」.