How does trading actually occurs in the stock market ?

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My understanding from the stock market is that at the same time we have multiple agents either selling or buying a stock. The sellers will communicate an ask price (the price at which they want to sell), and the buyers a bid price.

Both sellers and buyers want to transact different quantities and at different prices. How does the final price and quantity is decided for a transaction ?

For instance, suppose I want to sell 1000 units of stock A at the price of 1 but there is only a buyer willing to buy 500 units, do I only sell 500 or the transaction does not occur at all ?

Thanks

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