Old English bacan "to bake, to cook by dry heat in a closed place or on a heated surface," from Proto-Germanic *bakan "to bake" (source also of Old Norse baka, Middle Dutch backen, Old High German bahhan, German backen), from PIE *bheg- (source also of Greek phogein "to roast"), extended form of root *bhē- "to warm" (see bath). Related: Baked (Middle English had baken); baking. Baked beans attested by 1803.
word-forming element making nouns meaning "place for, art of, condition of, quantity of," from Middle English -erie, from Latin -arius (see -ary). Also sometimes in modern colloquial use "the collectivity of" or "an example of."
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Harper, D. (n.d.). Etymology of bakery. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/bakery