Its everyones favorite time again. Wisecrack's 8th grade hoborants about mathematics.

Lets start with the example

a=89
b=223
p=a*b=19847

If

(1/(5/p))/b = 17.8

and naturally

p/5 =3969.4

3969.4/b = 17.8

What I find interesting is that...

p/17.8 = 1115.0

..for any product and factors (given two factors), the result will always be an integer.

Why is this?

You can see that

t= 1115.0*b = 248645.0

And if

17.8*(p/a) = 3969.4

Then

17.8*(t/p) = 223.0 (our factor, b)

a*(t/p)
1115.0

p/1115
17.8

also a*(t/p) = 1115.0

I could be once again misunderstanding but
what it looks like is that theres some real number that always transforms p into an integer on the ring of integers (Z) representing multiples of the factors of p.

Now notice

b/17.8 = 12.52808988764045

We can also get that number like so..

t/p = 12.52808988764045
I think (though I could be mistaken) is that the reason is because t is b*1115 and 12.52808988764045 is the ratio between b and 17.8 as well as the ratio between
p and 1115.

And if we do

t/√p = 1764.9495488858483

1764.9495488858483^2 = 3115046.9101123596

also incidentally
3115046.9101123596/t =12.52808988764045
3115046.9101123596/12.52808988764045 =
t (this is obvious but I want to point it out anyway), or 248645.0

and

1115/b = 5.0

248645.0/5 = 49729.0

and

√49729.0 = b

Why is this last part true, that √(t/5) = b?