What is the difference between "Halb" and "Hälfte"?
What is the difference between "Halb" and "Hälfte"? I had been dismissing them as completely interchangeable for meaning "Half" , but I guess that's not the case? My first guess is that "Halb" is used as a prefix and "Hälfte" is not?

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"Die Hälfte (von X)" is mostly used when X is a specific object you are either pointing at or which was introduced before. On the other hand, "halb" denotes just half of something which is not specified in more detail. Examples:

"Die Hälfte von diesem Brot": One half of that particular loaf of bread I am pointing at.
"Ein halbes Brot": Just a half of any loaf of bread (assuming they are all more or less the same size).

"Die Hälfte vom Kuchen ist übrig geblieben": Half of the cake (that had been served for the meal) is left.
"ein halbes Kilo", "ein halber Meter", "eine halbe Sekunde" (works with any unit of measure)

And grammatically, "die Hälfte" is a noun, while "halb" is an adjective.

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All of that makes sense what with my seeing halb mainly as a prefix then. I should also have noticed that, on it's own, halb isn't capitalized, yet Hälfte always is. Thanks guys!

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Die Fahne steht auf Halbmast.
Ich komme um halb drei.
Ich habe noch eine halbe Pizza uebrig.

Gibst Du mir die Haelfte?
Mochtest Du die Haelfte?

Haelfte is used as a noun, halb is used more like a preposition