Does knowing how much 1 USD was worth in two currencies for a given date mean I can know how much they were worth in relation to each other?

Does knowing how much 1 USD was worth in two currencies for a given date mean I can know how much they were worth in relation to each other?

Yes, you can safely make this approximate assumption. If it were not the case, triangular arbitrage would have been possible. That would have made the currency prices fall in line such that you can make the assumption.

Does that mean that I can calculate how much 1 NOK was worth in MXN on that date?

Yes, at least approximately. It's simply the ratio of the two. On that day you can use 9.4015 MXN to buy 1 dollar and use that dollar to buy 7.9640 NOK. So you would have paid 9.4015 MXN for 7.9640 NOK. or 0.8471 NOK for 1 MXN.

In practice you couldn't do these actual transaction without paying substantial fees and exchange charges, but the math is still mostly correct.

Let's look at today: 1 USD = 8.83834 NOK and 1 USD = 20.0395 MXN we'd expect 1MXN to be 8.83834/20.0395 = 0.44105 NOK. The actual exchange rate quoted is 0.440540, so it's very close to our estimate.

Yes, you can. In my opinion the easiest way to work out how to do the sum is to use dimensional analysis.

Suppose you can by X NOK for 1 USD, and Y MXN for 1 USD.

This means you have:

• NOK/USD = X
• MXN/USD = Y

To know how NOK and MXN relate to each other, invert one of the values and multiply by the other so that the USDs cancel out:

• NOK/USD = X
• USD/MXN = 1/Y
• NOK/MXN = X/Y

So for 1 MXN you can buy X/Y NOK. Similarly for 1 NOK you can buy Y/X MXN.

In addition to other answers, I'd like to add that some currencies have pretty much fixed rate against usd (e.g. currencies of Gulf countries, UAE, Saudi Arabia, Panama etc). So for these countries you can do that transformation for longer times. For example, you know the rate of UAE dirham, and Saudi Riyal on 21 Jan 2015. Approximately the same ratio can should be valid for today as well.

One caveat is due to inflation or some other reason, these rates might change om rare occasions (like once in 20 year or so)

If 1 USD = 7.9640 NOK and 1 USD = 9.4015 MXN, that means that 7.9640 NOK = 9.4015 MXN. Therefore, 1 NOK = (9.4015/7.9640) MXN. That's about 1.1805 MXN.