"half the price" sounds odd to me. However, "half price" is okay. " The examples in part 2 of your post sound okay.
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RayH"half the price" sounds odd to me. However, "half price" is okay.
MrPernicketyThis gave me a ballpark idea that "half the price" is used only when we define the price (as it was done in the three sentences above).I agree. If the "price", whatever it is, is explicitly mentioned or is understood from the context then "half the price" is fine.
MrPernicketyPS: That goes to show that the articles in English is the biggest problem mankind has ever confronted in all of history !And here I was thinking it was prepositions.