A simple calculation will discover how much an amount of currency held is worth in terms of the other currency. Take a hypothetical exchange rate of USD/CHF = 1.3735

When you are holding base currency, you need to calculate how much this amount is worth in terms of quoted currency. So, to calculate how many CHF can be purchased with, say USD10 million; multiply the amount of base currency by the quoted exchange rate;

USD10 million x 1.3735 = CHF13,735,000.00

When you are holding quoted currency, you need to discover how much this amount is worth in terms of base currency. So, to calculate how many US dollars can be purchased with, say CHF10 million; divide the amount of quoted currency by the exchange rate;

10,000,000 / 1.3735 = USD 7,280,669.82

An exchange rate changes when one unit of the base currency buys more or less units of the quoted currency.  So if the USD/JPY rate changes from 112.85 to 113.14, one USD buys more yen. The dollar has strengthened or appreciated against the yen.

If the USD/JPY rate changes from 112.85 to 112.42, one USD buys less yen. The dollar has weakened or depreciated against the yen.

Changes in an exchange rate are measured by the formula:

So, for example, if USD/JPY moves from 112.85 to 113.14:

(113.14 - 112.85 / 112.85) x 100 = 0.0026

The USD has strengthened or appreciated by 0.26% (26 points) against the JPY.

Conversely, if USD/JPY moves from 112.85 to 112.42:

(112.42 - 112.85 / 112.85) x 100 = 0.0038

The USD has weakened or depreciated by 0.38% (38 points) against the JPY.

Market convention dictates that it is always the base currency which is said to strengthen or weaken (appreciate or depreciate), even though this is all relative and we could equally say that the yen has weakened or strengthened against the dollar. We do not say this because everything in FX is seen from the perspective of the base currency.