Discovering exchange rate based on the rates of others

Question

i'm trying to convert one currency to another, based on what that currency rate is to USD.

If 1 USD is 1.350297NZD, what is 1NZD to GBP if 1 USD is 0.70632 GBP

Answer 1

The common thread is $1$ USD. So \begin{align} 1\, \text{USD} &= 1.350297 \,\text{NZD} \\ &= 0.70632 \,\text{GBP} \\ \implies 1 \,\text{NZD} &= \left(\frac{0.70632}{1.350297}\right)\, \text{GBP} \\ &= 0.523085\, \text{GBP} \end{align}

Answer 2

Use unit cancellation. Then you don't have to remember when to multiply, when to divide. You want $$ \frac{? \text{ NZD}}{1 \text{ GBP}} = \frac{1.3... \text{ NZD}}{1 \text{ USD}} \times \frac{1\text{ USD}}{0.7... \text{GBP}}. $$ Then do the arithmetic. Invert if you want the other conversion.