1/2= 0.5
Secp256k1 curve, 1/2=
57896044618658097711785492504343953926418782139537452191302581570759080747169

3/2= 1.5
Secp256k1 curve, 3/2=
57896044618658097711785492504343953926418782139537452191302581570759080747170

When you operate mod n, 1.5 turns into 0.5+1, or half of n +1.  This is true for 1 up to n-1. Like 11/2 is just n/2+5.
So what about 51/2? It's  n/2+25, how about 701/2? It's n/2+350.  How about 1001/2? It's n/2+500.

Now moving forward, 10001/85= 117.65882
1/85= 0.011764706
Subtracting  0.011764706 - 117.65882 = 117.64706, not integer, now we want to know how to find 0.65882 of n, because 1/85 didn't give us 0.65882, it gives us 0.011764706, but  subtracting them gave us some clues, the answer is n.64706th+117.  We don't want our result to be a fraction, so we need to find the remainder of division mod n. 
Now going bigger, 1000001/85= 11764.718, 1000002/85=
 11764.729,   1000003/85= 11764.741,  1000004/85=
 11764.753.

See what happened?
0.011764706 1/85
0.011764718 1million and one/85, I added 0.0 - .
0.011764729 1million and two/85, added 0.0 - .
0.011764741 1m and three/85
0.011764753 1m and four/85
If you remove 0.0 from above fractions, you get the correct answer.