quouting and execution

lets asume price is 14.20, and someone is quoting 14.12, so i understand i could buy from someone at 14.12 to have a match?
 
Trade quotes are different from Bid/Ask. You would be buying the ask. If you make a bid somewhere in between the market bid/ask, someone may "hit" your bid and you then get a "fill".

That fill becomes the "last" quote.
 
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