From my understanding, absent "ちうわけで", this simply means, "Is it OK if I go to break." Is it similar to "こういうわけで"?
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Related (see the part near the end): japanese.stackexchange.com/a/2258/5010– narutoAug 25, 2018 at 5:47
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2My guess is that this is slurred というわけで, but I'm no linguist, just going by the sound of it. Or maybe it's dialectical? My brief search hasn't turned out anything, but that's not much of a proof (where is this from btw?)– NoxArtAug 25, 2018 at 6:00
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It's from のんのんびより– Anthony HardmanAug 25, 2018 at 6:09
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1ちゅわけで is a colloquial contraction of というわけで– KurausukunAug 25, 2018 at 7:57
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From the context, it can't be anything else but a slurred というわけで as NoxArt guessed– DXVAug 28, 2018 at 1:31
1 Answer
ちう (and ちゅう) is a slurred version of という, so ちうわけで is the same as というわけで.
というわけで basically just means "So, ..." or "For that reason, ...". It's mainly used to describe a conclusion after stating a reason. It's also used to draw the listeners' attention before moving on to the main topic (e.g., "So, let's start today's lesson"). Sometimes it's used even at the very beginning of an exchange (like English "So, hello, my name is ...").
From this answer:
というわけで、…
So with that, …This is especially common in TV or radio shows when the host needs to press the show forward or move on to the next topic. The という wraps up the preceding statements into わけ and essentially means, "Now that all this has been said, let's move on."