It's not as unusual as you think, and it's not even very awkward to say (at least to me, being a native English speaker).
It is indeed contracted just like that, "where're."
"Where're you going?" is probably the most common usage.
Remember contractions are always considered at least a little informal, so don't say this if you're trying to deliver grave news or a formal speech.
I don't keep statistics, but if I had to guess I would say that where're is not as popular as it once was in vernacular. I think it's also more commonly said by children, who sometimes slur syllables together since they're not as experienced using the language.
From The Cambridge Grammar of the English Language, p.1614:
Prepositions, auxiliaries, and infinitival to are stressed when they are the sole or final element in a phrase-level constituent, a PP or VP [preposition phrase or verb phrase].
Note that be is always an auxiliary verb. In your example, is is an auxiliary at the end of a verb phrase:
1a. If it is ___ then replace the frobulator.
1b. *If it's ___ then replace the frobulator. ← ungrammatical
If we added the ellipted word spinning back in, it would no longer be at the end of the phrase, and it would be possible to contract it:
2a. If it is spinning then replace the frobulator.
2b. If it's spinning then replace the frobulator.
This is the same reason you can't reduce it is to it's at the end of a sentence. Is needs to bear stress, so it can't be reduced to clitic form (can't be contracted).
In this answer, the * symbol means that a sentence is ungrammatical.
The two sentences mean the same exact thing. However, as a native English speaker in the US, I would absolutely say it's far more common to hear You're welcome.
You are welcome is a phrase I've said on multiple occasions, but it was to stress the sincerity of the statement. Actually saying "you are" rather than the contraction "you're" is unusual, which is why I specifically used it to stress the meaning.
In regular conversations, you'll almost always hear "You're welcome".
Best Answer
It's not as unusual as you think, and it's not even very awkward to say (at least to me, being a native English speaker).
It is indeed contracted just like that, "where're."
"Where're you going?" is probably the most common usage. Remember contractions are always considered at least a little informal, so don't say this if you're trying to deliver grave news or a formal speech.
I don't keep statistics, but if I had to guess I would say that where're is not as popular as it once was in vernacular. I think it's also more commonly said by children, who sometimes slur syllables together since they're not as experienced using the language.