The never-ending division shows prudence (6)
I believe the answer is:
thrift
'prudence' is the definition.
(I know that thrift is a type of frugality)
'the never-ending division' is the wordplay.
'never ending' means to remove the last letter.
'division' becomes 'rift' (I've seen this in another clue).
'the' with its last letter taken off is 'th'.
'th'+'rift'='THRIFT'
'shows' acts as a link.
(Other definitions for thrift that I've seen before include "Scrimping and scraping" , "Careful spending" , "Economy - sea pink" , "Taking care of money" , "Maritime growth" .)