J, 84 bytes
Will golf furtherStarting from a 1 element list the function keeps all the possible intermediate numbers in the list by evaling the next expression and add explanation tomorrowadding it's up and down rounded copies.
Will golf further and add explanation tomorrow.
Can't find obvious ways to golf it more.
f=.3 :'/:~~.<.>((,>.,<.)@".@(":@],''x'',;@[))&.>/|.(>@{.;_2<\}.);:y rplc''/'';''%'''
Passes all the tests.
Usage:
f '1/3*2*2*2*2*2*2'
0 16 20 21 22 24 32 64
f '1/3*9'
0 3 9