So, forgive my ignorance, this isn't a troll just a question.

How are continued fractions related to modular arithmetic?

Take the following example:

70%32 = 6
70//32 = 2

which we can just represent as
6+(32*2)

Now, as a continued fraction, we would do

70/32 = 2 + 6/32
and repeating what we just did but for 6/32, as you would with a continued fraction.

Am I actually doing everything correctly here or am I missing something?