Delta Hedging

I am trying to compare delta heding in schweser book 4 versus that in book 5. In book 4 we have a dealer who is short a call and wants to cover the call by buying delta shares for every call option short. In equation form: 1 short call = delta shares 10,000 short calls = delta * 10,000 I sort of understand this: Now going into Book5, using an option to delta hedge a currency position. So, the scene is that you (US Investor) have invested money in the UK and want to hedge against pound depreciation. So, the solution is to use a put option - I get that. But the number of put options to buy is -(1/delta). This is where the confusion begins. I think the answer is as below but I am not at all sure: we are buying (1/delta) because when compared to book4, we were short calls and hence had to buy delta shares. Now, we have the shares (currrency) and we have to buy the options, hence (1/delta). But why the negative sign. I know this is not the most important part of the exam but just intel. curious - any thoughts!

calls vs puts. If you are hedging a long exposure with puts you are buying puts. A put has a negative delta (i.e., stock goes up, put value goes down). Thus, for a put -1/delta is positive.

that was helpful, thanks