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What are the differences between wakata wakatteru wakarimashita

wakata past positive plain tense did understand
wakarimashita past positive polite tense
now i try to guess.
since eru is potential form, wakata+eru=wakatteru could understand

it should be wakatta
wakarimashita is exactly as was said above
wakatteru - iru after a verb in the te form is often colloquially shortened to just "ru", so this is actually "wakatte iru" which is present progressive. It literally means "I am understanding". You could use this to say that you already understand something somebody is telling you, among other things.

Fast I'm japanese. but my English is poor.

”wakatta" means "follow you","just now I understand","OK"　case by case.

"wakatteru" means "I have already understood(known)", "Of course".

"wakarimashita" is civil."wakarimashita" means "wakatta"

If you meet a older than you ,you say "wakarimashita", not "wakatta".

wakatta = I get it now (I didn't understand it before you explained it to me)
wakarimashita = wakatta

wakatte iru = I know! (I already know, you don't need to explain)

Example: Sou iwarenakute mo wakatteru yo! = Don't talk to me like I'm an idiot!