I’m a “quarter past” person but I’ve always been confused by “half ten” (which thankfully isn’t used in Australia). But in German, “half ten” means 9:30, which is make more sense to me (probably because I’m used to how German speech often drops words, which is less common in English)

For "half ten" we're just dropping a word from "half past ten".

How does one get to "half ten" in German? Is it simply starting from "half to ten"?