Currency conversion using available rates

Question

I have the following rates available:

USD -> USD = 1
USD -> EUR = 0.887662
USD -> GBP = 0.654514

I want to calculate the following rates

GBP -> EUR
EUR -> GBP

Using only the first 3 rates.

My process so far has been:

1 USD / 0.654514 GBP = 1.527851
So
1 GBP = 1.53 USD

1 USD / 0.887662 = 1.126554
So
1 EUR = 1.13 USD

I assume I have all the data needed now to calculate the following conversions

GBP -> EUR
EUR -> GBP

From this point however, I am not sure how to continue.

Answer 1

We know the exchange rates $\frac{$}{€}=0.887662$ and $\frac{$}{£}=0.654514$. So we have

$$ \frac{€}{£}=\frac{$}{£}\times\frac{€}{$}=\frac{$}{£}\times \frac{1}{$/€}=0.654514\times \frac{1}{0.887662}=\frac{0.654514}{0.887662}=0.737346 $$ and $$ \frac{£}{€}= \frac{1}{€/£}=\frac{1}{0.737346}=1.356215 $$