If 1 british pound equals 1.6972 swiss francs, then 1 swiss franc equals approximately how many british pounds?

Start with "1 British pound equals 1.6972 Swiss francs" and make a conversion factor out of it:

1.6972 Sw. F.

 1 Br. pound

Invert this, obtaining:  

 1 Br. pound

1.6972 Sw. F.

Here's where the fun begins.  To find the value of 1 SFr in BPS, mult.

1 SFr by the above conversion factor:

1 SFr             1 BPS
* = 0.5892 BPS
      1          1.6972 Sw. F.

This is a formal way in which to do this problem.  You could obtain the same result if you'd simply invert 

 1 Br. pound
= 1
1.6972 Sw. F. 

and divide 1 by 1.6972.