How many fractions?

[greatwhiteshark]

Arrange all the fractions of the form m/n in a row where m and n are
counting numbers and satisfy the following conditions:

A) If a×b < m2×n2, then m1/n1 must be placed before m2/n2.
B) If m1×n1 = m2×n2 and n1<n2, then m1/n1 must also be placed before m2/n2.

How many fractions are there between 1998/1 and 1/1998?

 

[Gene]

Using the standard way of listing all fractions where m+n < 5+1 you get

              1/1
            1/2 2/1
          1/3 2/2 3/1
        1/4 2/3 3/2 4/1 
      1/5 2/4 3/3 4/2 5/1
           .........

For your case you seem to want m<n<5 so you would continue

        2/5 3/4 4/3 5/2
          3/5 4/4 5/3
            4/5 5/4
              5/5

I don't understand where your order comes in but this should show you how to find how many. If you mean something else, let me know. There are an infinite number between any two fractions without some rule like mine.

 

[Denis]

A) If a×b < m2×n2, then m1/n1 must be placed before m2/n2.

Hmmm...what's "a" and "b" ? may I ask.