In Bulgarian both "homework" and "work" are countable. Why are they uncountable in English then? What is the difference in meaning that makes that happen?
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Both are considered mass nouns, just like milk, air, etc.
However, work can also refer to a singular piece of creation (art, literature, plays, etc.), in which case it can be pluralized:
If you want to refer to a specific part of your work, you could use task:
Likewise, if you want to refer to a single, discrete unit of homework, use assignment: