# cross rates

i cannot seem to grasp cross rates. sometimes you divide the two and sometimes you multiply and i am completely lost when to do which.

any pointers?

If you always write both currencies when they give you an exchange rate, you cannot make a mistake. For example, suppose that they give you \$1.2890/€ and \$1.5253/£ and ask for the £/€ exchange rate. You need £ in the numerator and € in the denominator, so the calculation is:

1£/\$1.5253 × \$1.2890/€ = 0.8451£/€.

By including both currencies in each exchange rate you cannot make the mistake of dividing 1.2890 by 1.5253, nor of multiplying them together.

that is from s2000 in a previous thread.

why is it 1GBP to \$1.5253 in the answer but opposite in the question?

for some reason i cannot grasp exchange rates at all

Always write the currencies. Both currencies.

Suppose that you’re given these rates:

• BRL/AUD 2.1389
• BRL/EUR 3.2273

This means BRL2.1389/AUD and BRL3.2273/EUR. If you want to know the EUR/AUD exchange rate, you write:

BRL2.1389/AUD × EUR/3.2273BRL = EUR0.6628/AUD

The BRL in the numerator in the first factor cancels with the BRL in the denominator in the second factor, leaving you with EUR2.1389 in the numerator and AUD3.2273 in the denominator; 2.1389 ÷ 3.2273 = 0.6628.

It’s simply the stupid convention for writing exchange rates. “USD/GBP1.5253” means \$1.5253/£. That’s just the way they write it. Sorry.

(PS: I just typed a response and posted it, then say that someone (you, as it turns out), already posted a response. I started to read it and thought, “Wow! This guy uses ‘£’ and ‘×’, the same as I would. That’s really interesting. I should probably delete my reply as he’s already written what I just wrote.” Then I read further. )

how do you that brl is the numerator for brl/aud and the denominator in eur/brl?

If you do it the other way around, you end up with AUD/EUR. We’re looking for EUR/AUD, so we need EUR in the numerator, and AUD in the denominator. That tells us what to do with each exchange rate we’ve been given.