From Forth, here's how I'd set the rationals:
: gcd begin dup while tuck mod repeat drop ;
: lcm 2dup \* abs -rot gcd / ;
: reduce 2dup gcd tuck / >r / r> ;
: q+ rot 2dup \* >r rot \* -rot \* + r> reduce ;
: q- swap negate swap q+ ;
: q\* rot \* >r \* r> reduce ;
: q/ >r \* swap r> \* swap reduce ;
Example: to compute 70 * 0.25 = 35/2
70 1 1 4 q* reduce .s
35 2 ok
On stack managing words like 2dup, rot and such, these are easily
grasped under either Google/DDG or any Forth with the words "see" and/or "help".
as a hint, q- swaps the top two numbers in the stack, (which compose a rational), makes the last one negative and then turns back its position. And then it calls q+.
So, 2/5 - 3/2 = 2/5 + -3/2.
