A fat is fatty acid molecules held together with a glycerol bond. Point a couple fingers up, the fingers are the fatty acids, and your knuckles are the bond. Making soap breaks this bond, stripping off the glycerol, leaving you with a bunch of fatty acid salts (individual fingers floating around, sans knuckles). Because that bond isn’t there anymore, one end of the fatty acid salt, or “soap,” molecule still likes fat, but the other end now likes water.
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