each person or thing gets an equal share or amount, one per individual.
From Middle English 'a piece,' combining 'a' (one) and 'piece' (part). Originally meant literally one piece to each person, evolving to mean per unit or per individual.
This word is a fossil of how English used to split phrases differently—'apiece' was once two words but fused together, similar to how 'a lot' might someday become 'alot.' It's a rare example of language compounding in modern English.
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