Scheme - “inexact” concept in R5RS numerical tower

Question

While thinking about the way to implement Scheme R5RS, I have become puzzled about the following extract of R5RS (pages 22-23):

(remainder -13 -4) ==> -1
(remainder -13 -4.0) ==> -1.0 ; inexact

(lcm 32 -36) ==> 288
(lcm 32.0 -36) ==> 288.0 ; inexact

(denominator (/ 6 4)) ==> 2
(denominator (exact->inexact (/ 6 4))) ==> 2.0

Should we understand that, even if -4.0, 32.0 and (exact->inexact (/ 6 4)) are inexact, the implementation shall "remember" their exact equivalent (-4, 32 and 3/2) in order to proceed to integer division, prime factors decomposition, etc?

Otherwise, how could the implementation succeed in giving the above answers?

Thanks in advance for any light you could throw on this subject! :)

Nicolas