how is the token pricing coordinated?

txholdem

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on one exchange there are many different pairs.

suppose ETH is 10 LTC, and 0.1BTC. how is LTC simultaneously traded for 0.01 BTC?
all the trades happen at the same time. some trade between LTC/ETH, some trade ETH/BTC, and some trade LTC/BTC.

i look at the prices of say XRP in USD, on the XRP/BTC pair, and the XRP/ETH pair, and they are exactly the same, down to the last digit. how?
 
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