Fractions On A Number Line

Directions: Using the digits 0 to 5 at most one time each, place a digit to create five fractions and place them all on a number line with the correct order and spacing.

Hint

Which

Answer

There are many ways to approach this problem. For example students might use random digits and then carefully measure a whole into equal portions to determine placement. Alternatively, students might get strategically creative and do things like create the fractions 2/2, 3/3, 1/4, 0/6, and 4/8 so that they only have to place 1, 1, 1/4, 0, and 1/2.

Source: Robert Kaplinsky

Check Also

Make The Time

Directions: Using the digits 0 to 9 at most one time each, place a digit …

9 comments

  1. 1\2 2\3 3/4 4/6 5/8

  2. 1/2 2/3 3/4 4/6 5/8

  3. Hello,
    Fractions On A Number Line needs a hint written please.

  4. 1 3 5 4 0

    ————————————————————————
    2 3 4 6 8

  5. 1/2/2 and a half/3/3 in a half/4/5/5 in a half/6/7/8

  6. 1/2 2/3 3/3 5/6 4/7 3/8

  7. Rudolf Österreicher

    There are 720 different number lines that can be the result of this exercise (not counting for example a = b < x < y < z as different from b = a < x < y < z):
    0/2 < 1/3 < 2/4 < 5/8 < 4/6
    0/2 < 1/3 < 2/4 = 3/6 < 5/8
    0/2 < 1/3 < 2/4 = 3/6 = 4/8
    0/2 < 1/3 < 2/4 = 4/8 < 5/6
    0/2 < 1/3 < 3/6 < 5/8 < 4/4
    0/2 < 1/3 < 3/6 = 4/8 < 5/4
    0/2 < 1/3 < 3/8 < 2/4 < 4/6
    0/2 < 1/3 < 3/8 < 2/4 < 5/6
    0/2 < 1/3 < 3/8 < 4/6 < 5/4
    0/2 < 1/3 < 3/8 < 5/6 < 4/4
    0/2 < 1/3 < 4/8 < 3/4 < 5/6
    0/2 < 1/3 < 5/8 < 4/6 < 3/4
    0/2 < 1/3 = 2/6 < 3/8 < 4/4
    0/2 < 1/3 = 2/6 < 3/8 < 5/4
    0/2 < 1/3 = 2/6 < 4/8 < 3/4
    0/2 < 1/3 = 2/6 < 4/8 < 5/4
    0/2 < 1/3 = 2/6 < 5/8 < 3/4
    0/2 < 1/3 = 2/6 < 5/8 < 4/4
    0/2 < 1/4 < 2/6 < 3/8 < 4/3
    0/2 < 1/4 < 2/6 < 3/8 < 5/3
    0/2 < 1/4 < 2/6 < 4/8 < 3/3
    0/2 < 1/4 < 2/6 < 4/8 < 5/3
    0/2 < 1/4 < 2/6 < 5/8 < 3/3
    0/2 < 1/4 < 2/6 < 5/8 < 4/3
    0/2 < 1/4 < 3/6 < 5/8 < 2/3
    0/2 < 1/4 < 3/6 < 5/8 < 4/3
    0/2 < 1/4 < 3/6 = 4/8 < 2/3
    0/2 < 1/4 < 3/6 = 4/8 < 5/3
    0/2 < 1/4 < 3/8 < 2/3 < 5/6
    0/2 < 1/4 < 3/8 < 2/3 = 4/6
    0/2 < 1/4 < 3/8 < 4/6 < 5/3
    0/2 < 1/4 < 3/8 < 5/6 < 4/3
    0/2 < 1/4 < 4/8 < 2/3 < 5/6
    0/2 < 1/4 < 4/8 < 5/6 < 3/3
    0/2 < 1/4 < 5/8 < 2/3 = 4/6
    0/2 < 1/4 < 5/8 < 4/6 < 3/3
    0/2 < 1/4 = 2/8 < 3/6 < 4/3
    0/2 < 1/4 = 2/8 < 3/6 < 5/3
    0/2 < 1/4 = 2/8 < 4/6 < 3/3
    0/2 < 1/4 = 2/8 < 4/6 < 5/3
    0/2 < 1/4 = 2/8 < 5/6 < 3/3
    0/2 < 1/4 = 2/8 < 5/6 < 4/3
    0/2 < 1/6 < 2/4 < 5/8 < 3/3
    0/2 < 1/6 < 2/4 < 5/8 < 4/3
    0/2 < 1/6 < 2/4 = 4/8 < 3/3
    0/2 < 1/6 < 2/4 = 4/8 < 5/3
    0/2 < 1/6 < 2/8 < 3/3 < 5/4
    0/2 < 1/6 < 2/8 < 3/3 = 4/4
    0/2 < 1/6 < 2/8 < 3/4 < 4/3
    0/2 < 1/6 < 2/8 < 3/4 < 5/3
    0/2 < 1/6 < 2/8 < 4/4 < 5/3
    0/2 < 1/6 < 2/8 < 5/4 < 4/3
    0/2 < 1/6 < 3/8 < 2/3 < 4/4
    0/2 < 1/6 < 3/8 < 2/3 < 5/4
    0/2 < 1/6 < 3/8 < 2/4 < 4/3
    0/2 < 1/6 < 3/8 < 2/4 < 5/3
    0/2 < 1/6 < 3/8 < 4/4 < 5/3
    0/2 < 1/6 < 3/8 < 5/4 < 4/3
    0/2 < 1/6 < 4/8 < 2/3 < 3/4
    0/2 < 1/6 < 4/8 < 2/3 < 5/4
    0/2 < 1/6 < 4/8 < 3/3 < 5/4
    0/2 < 1/6 < 4/8 < 3/4 < 5/3
    0/2 < 1/6 < 5/8 < 2/3 < 3/4
    0/2 < 1/6 < 5/8 < 2/3 < 4/4
    0/2 < 1/6 < 5/8 < 3/3 = 4/4
    0/2 < 1/6 < 5/8 < 3/4 < 4/3
    0/2 < 1/8 < 2/3 < 3/4 < 5/6
    0/2 < 1/8 < 2/3 < 5/6 < 4/4
    0/2 < 1/8 < 2/3 = 4/6 < 3/4
    0/2 < 1/8 < 2/3 = 4/6 < 5/4
    0/2 < 1/8 < 2/4 < 4/6 < 3/3
    0/2 < 1/8 < 2/4 < 4/6 < 5/3
    0/2 < 1/8 < 2/4 < 5/6 < 3/3
    0/2 < 1/8 < 2/4 < 5/6 < 4/3
    0/2 < 1/8 < 2/4 = 3/6 < 4/3
    0/2 < 1/8 < 2/4 = 3/6 < 5/3
    0/2 < 1/8 < 2/6 < 3/3 < 5/4
    0/2 < 1/8 < 2/6 < 3/3 = 4/4
    0/2 < 1/8 < 2/6 < 3/4 < 4/3
    0/2 < 1/8 < 2/6 < 3/4 < 5/3
    0/2 < 1/8 < 2/6 < 4/4 < 5/3
    0/2 < 1/8 < 2/6 < 5/4 < 4/3
    0/2 < 1/8 < 3/4 < 5/6 < 4/3
    0/2 < 1/8 < 3/6 < 2/3 < 4/4
    0/2 < 1/8 < 3/6 < 2/3 < 5/4
    0/2 < 1/8 < 3/6 < 4/4 < 5/3
    0/2 < 1/8 < 3/6 < 5/4 < 4/3
    0/2 < 1/8 < 4/6 < 3/3 < 5/4
    0/2 < 1/8 < 4/6 < 3/4 < 5/3
    0/2 < 1/8 < 5/6 < 3/3 = 4/4
    0/2 < 2/4 < 5/8 < 4/6 < 3/3
    0/2 < 2/4 = 3/6 < 5/8 < 4/3
    0/2 < 2/4 = 3/6 = 4/8 < 5/3
    0/2 < 2/4 = 4/8 < 5/6 < 3/3
    0/2 < 2/6 < 3/8 < 4/4 < 5/3
    0/2 < 2/6 < 3/8 < 5/4 < 4/3
    0/2 < 2/6 < 4/8 < 3/3 < 5/4
    0/2 < 2/6 < 4/8 < 3/4 < 5/3
    0/2 < 2/6 < 5/8 < 3/3 = 4/4
    0/2 < 2/6 < 5/8 < 3/4 < 4/3
    0/2 < 2/8 < 1/3 < 3/4 < 5/6
    0/2 < 2/8 < 1/3 < 3/6 < 4/4
    0/2 < 2/8 < 1/3 < 3/6 < 5/4
    0/2 < 2/8 < 1/3 < 4/6 < 3/4
    0/2 < 2/8 < 1/3 < 4/6 < 5/4
    0/2 < 2/8 < 1/3 < 5/6 < 4/4
    0/2 < 2/8 < 3/4 < 5/6 < 4/3
    0/2 < 2/8 < 3/6 < 4/4 < 5/3
    0/2 < 2/8 < 3/6 < 5/4 < 4/3
    0/2 < 2/8 < 4/6 < 3/3 < 5/4
    0/2 < 2/8 < 4/6 < 3/4 < 5/3
    0/2 < 2/8 < 5/6 < 3/3 = 4/4
    0/2 < 3/6 < 5/8 < 2/3 < 4/4
    0/2 < 3/6 = 4/8 < 2/3 < 5/4
    0/2 < 3/8 < 2/3 < 5/6 < 4/4
    0/2 < 3/8 < 2/3 = 4/6 < 5/4
    0/2 < 3/8 < 2/4 < 4/6 < 5/3
    0/2 < 3/8 < 2/4 < 5/6 < 4/3
    0/2 < 4/8 < 2/3 < 3/4 < 5/6
    0/2 < 5/8 < 2/3 = 4/6 < 3/4
    0/3 < 1/2 < 5/8 < 4/6 < 3/4
    0/3 < 1/2 = 2/4 < 5/8 < 4/6
    0/3 < 1/2 = 2/4 = 3/6 < 5/8
    0/3 < 1/2 = 2/4 = 3/6 = 4/8
    0/3 < 1/2 = 2/4 = 4/8 < 5/6
    0/3 < 1/2 = 3/6 < 5/8 < 4/4
    0/3 < 1/2 = 3/6 = 4/8 < 5/4
    0/3 < 1/2 = 4/8 < 3/4 < 5/6
    0/3 < 1/4 < 2/6 < 3/8 < 4/2
    0/3 < 1/4 < 2/6 < 3/8 < 5/2
    0/3 < 1/4 < 2/6 < 4/8 < 3/2
    0/3 < 1/4 < 2/6 < 4/8 < 5/2
    0/3 < 1/4 < 2/6 < 5/8 < 3/2
    0/3 < 1/4 < 2/6 < 5/8 < 4/2
    0/3 < 1/4 < 3/6 < 5/8 < 2/2
    0/3 < 1/4 < 3/6 < 5/8 < 4/2
    0/3 < 1/4 < 3/6 = 4/8 < 2/2
    0/3 < 1/4 < 3/6 = 4/8 < 5/2
    0/3 < 1/4 < 3/8 < 4/6 < 2/2
    0/3 < 1/4 < 3/8 < 4/6 < 5/2
    0/3 < 1/4 < 3/8 < 5/6 < 2/2
    0/3 < 1/4 < 3/8 < 5/6 < 4/2
    0/3 < 1/4 < 4/8 < 5/6 < 2/2
    0/3 < 1/4 < 4/8 < 5/6 < 3/2
    0/3 < 1/4 < 5/8 < 4/6 < 2/2
    0/3 < 1/4 < 5/8 < 4/6 < 3/2
    0/3 < 1/4 = 2/8 < 3/6 < 4/2
    0/3 < 1/4 = 2/8 < 3/6 < 5/2
    0/3 < 1/4 = 2/8 < 4/6 < 3/2
    0/3 < 1/4 = 2/8 < 4/6 < 5/2
    0/3 < 1/4 = 2/8 < 5/6 < 3/2
    0/3 < 1/4 = 2/8 < 5/6 < 4/2
    0/3 < 1/6 < 2/4 < 5/8 < 3/2
    0/3 < 1/6 < 2/4 < 5/8 < 4/2
    0/3 < 1/6 < 2/4 = 4/8 < 3/2
    0/3 < 1/6 < 2/4 = 4/8 < 5/2
    0/3 < 1/6 < 2/8 < 3/4 < 4/2
    0/3 < 1/6 < 2/8 < 3/4 < 5/2
    0/3 < 1/6 < 2/8 < 4/4 < 3/2
    0/3 < 1/6 < 2/8 < 4/4 < 5/2
    0/3 < 1/6 < 2/8 < 5/4 < 3/2
    0/3 < 1/6 < 2/8 < 5/4 < 4/2
    0/3 < 1/6 < 3/8 < 2/2 < 5/4
    0/3 < 1/6 < 3/8 < 2/2 = 4/4
    0/3 < 1/6 < 3/8 < 2/4 < 4/2
    0/3 < 1/6 < 3/8 < 2/4 < 5/2
    0/3 < 1/6 < 3/8 < 4/4 < 5/2
    0/3 < 1/6 < 3/8 < 5/4 < 4/2
    0/3 < 1/6 < 4/8 < 2/2 < 5/4
    0/3 < 1/6 < 4/8 < 3/4 < 2/2
    0/3 < 1/6 < 4/8 < 3/4 < 5/2
    0/3 < 1/6 < 4/8 < 5/4 < 3/2
    0/3 < 1/6 < 5/8 < 2/2 = 4/4
    0/3 < 1/6 < 5/8 < 3/4 < 2/2
    0/3 < 1/6 < 5/8 < 3/4 < 4/2
    0/3 < 1/6 < 5/8 < 4/4 < 3/2
    0/3 < 1/8 < 2/4 < 4/6 < 3/2
    0/3 < 1/8 < 2/4 < 4/6 < 5/2
    0/3 < 1/8 < 2/4 < 5/6 < 3/2
    0/3 < 1/8 < 2/4 < 5/6 < 4/2
    0/3 < 1/8 < 2/4 = 3/6 < 4/2
    0/3 < 1/8 < 2/4 = 3/6 < 5/2
    0/3 < 1/8 < 2/6 < 3/4 < 4/2
    0/3 < 1/8 < 2/6 < 3/4 < 5/2
    0/3 < 1/8 < 2/6 < 4/4 < 3/2
    0/3 < 1/8 < 2/6 < 4/4 < 5/2
    0/3 < 1/8 < 2/6 < 5/4 < 3/2
    0/3 < 1/8 < 2/6 < 5/4 < 4/2
    0/3 < 1/8 < 3/4 < 5/6 < 2/2
    0/3 < 1/8 < 3/4 < 5/6 < 4/2
    0/3 < 1/8 < 3/6 < 2/2 < 5/4
    0/3 < 1/8 < 3/6 < 2/2 = 4/4
    0/3 < 1/8 < 3/6 < 4/4 < 5/2
    0/3 < 1/8 < 3/6 < 5/4 < 4/2
    0/3 < 1/8 < 4/6 < 2/2 < 5/4
    0/3 < 1/8 < 4/6 < 3/4 < 2/2
    0/3 < 1/8 < 4/6 < 3/4 < 5/2
    0/3 < 1/8 < 4/6 < 5/4 < 3/2
    0/3 < 1/8 < 5/6 < 2/2 = 4/4
    0/3 < 1/8 < 5/6 < 4/4 < 3/2
    0/3 < 2/4 < 5/8 < 4/6 < 3/2
    0/3 < 2/4 = 3/6 < 5/8 < 4/2
    0/3 < 2/4 = 3/6 = 4/8 < 5/2
    0/3 < 2/4 = 4/8 < 5/6 < 3/2
    0/3 < 2/6 < 1/2 < 5/8 < 3/4
    0/3 < 2/6 < 1/2 < 5/8 < 4/4
    0/3 < 2/6 < 1/2 = 4/8 < 3/4
    0/3 < 2/6 < 1/2 = 4/8 < 5/4
    0/3 < 2/6 < 3/8 < 1/2 < 4/4
    0/3 < 2/6 < 3/8 < 1/2 < 5/4
    0/3 < 2/6 < 3/8 < 4/4 < 5/2
    0/3 < 2/6 < 3/8 < 5/4 < 4/2
    0/3 < 2/6 < 4/8 < 3/4 < 5/2
    0/3 < 2/6 < 4/8 < 5/4 < 3/2
    0/3 < 2/6 < 5/8 < 3/4 < 4/2
    0/3 < 2/6 < 5/8 < 4/4 < 3/2
    0/3 < 2/8 < 1/2 < 3/4 < 5/6
    0/3 < 2/8 < 1/2 < 4/6 < 3/4
    0/3 < 2/8 < 1/2 < 4/6 < 5/4
    0/3 < 2/8 < 1/2 < 5/6 < 4/4
    0/3 < 2/8 < 1/2 = 3/6 < 4/4
    0/3 < 2/8 < 1/2 = 3/6 < 5/4
    0/3 < 2/8 < 3/4 < 5/6 < 4/2
    0/3 < 2/8 < 3/6 < 4/4 < 5/2
    0/3 < 2/8 < 3/6 < 5/4 < 4/2
    0/3 < 2/8 < 4/6 < 3/4 < 5/2
    0/3 < 2/8 < 4/6 < 5/4 < 3/2
    0/3 < 2/8 < 5/6 < 4/4 < 3/2
    0/3 < 3/6 < 5/8 < 2/2 = 4/4
    0/3 < 3/6 = 4/8 < 2/2 < 5/4
    0/3 < 3/8 < 1/2 < 4/6 < 5/4
    0/3 < 3/8 < 1/2 < 5/6 < 4/4
    0/3 < 3/8 < 1/2 = 2/4 < 4/6
    0/3 < 3/8 < 1/2 = 2/4 < 5/6
    0/3 < 3/8 < 2/4 < 4/6 < 5/2
    0/3 < 3/8 < 2/4 < 5/6 < 4/2
    0/3 < 3/8 < 4/6 < 2/2 < 5/4
    0/3 < 3/8 < 5/6 < 2/2 = 4/4
    0/3 < 4/8 < 3/4 < 5/6 < 2/2
    0/3 < 5/8 < 4/6 < 3/4 < 2/2
    0/4 < 1/2 < 5/8 < 2/3 = 4/6
    0/4 < 1/2 < 5/8 < 4/6 < 3/3
    0/4 < 1/2 = 3/6 < 5/8 < 2/3
    0/4 < 1/2 = 3/6 < 5/8 < 4/3
    0/4 < 1/2 = 3/6 = 4/8 < 2/3
    0/4 < 1/2 = 3/6 = 4/8 < 5/3
    0/4 < 1/2 = 4/8 < 2/3 < 5/6
    0/4 < 1/2 = 4/8 < 5/6 < 3/3
    0/4 < 1/3 < 3/6 < 5/8 < 2/2
    0/4 < 1/3 < 3/6 < 5/8 < 4/2
    0/4 < 1/3 < 3/6 = 4/8 < 2/2
    0/4 < 1/3 < 3/6 = 4/8 < 5/2
    0/4 < 1/3 < 3/8 < 4/6 < 2/2
    0/4 < 1/3 < 3/8 < 4/6 < 5/2
    0/4 < 1/3 < 3/8 < 5/6 < 2/2
    0/4 < 1/3 < 3/8 < 5/6 < 4/2
    0/4 < 1/3 < 4/8 < 5/6 < 2/2
    0/4 < 1/3 < 4/8 < 5/6 < 3/2
    0/4 < 1/3 < 5/8 < 4/6 < 2/2
    0/4 < 1/3 < 5/8 < 4/6 < 3/2
    0/4 < 1/3 = 2/6 < 3/8 < 4/2
    0/4 < 1/3 = 2/6 < 3/8 < 5/2
    0/4 < 1/3 = 2/6 < 4/8 < 3/2
    0/4 < 1/3 = 2/6 < 4/8 < 5/2
    0/4 < 1/3 = 2/6 < 5/8 < 3/2
    0/4 < 1/3 = 2/6 < 5/8 < 4/2
    0/4 < 1/6 < 2/8 < 3/2 < 5/3
    0/4 < 1/6 < 2/8 < 3/3 < 4/2
    0/4 < 1/6 < 2/8 < 3/3 < 5/2
    0/4 < 1/6 < 2/8 < 4/3 < 3/2
    0/4 < 1/6 < 2/8 < 4/3 < 5/2
    0/4 < 1/6 < 2/8 < 5/3 < 4/2
    0/4 < 1/6 < 3/8 < 2/2 < 4/3
    0/4 < 1/6 < 3/8 < 2/2 < 5/3
    0/4 < 1/6 < 3/8 < 2/3 < 4/2
    0/4 < 1/6 < 3/8 < 2/3 < 5/2
    0/4 < 1/6 < 3/8 < 4/3 < 5/2
    0/4 < 1/6 < 3/8 < 5/3 < 4/2
    0/4 < 1/6 < 4/8 < 2/2 < 5/3
    0/4 < 1/6 < 4/8 < 2/2 = 3/3
    0/4 < 1/6 < 4/8 < 2/3 < 3/2
    0/4 < 1/6 < 4/8 < 2/3 < 5/2
    0/4 < 1/6 < 4/8 < 3/2 < 5/3
    0/4 < 1/6 < 4/8 < 3/3 < 5/2
    0/4 < 1/6 < 5/8 < 2/2 < 4/3
    0/4 < 1/6 < 5/8 < 2/2 = 3/3
    0/4 < 1/6 < 5/8 < 2/3 < 3/2
    0/4 < 1/6 < 5/8 < 2/3 < 4/2
    0/4 < 1/6 < 5/8 < 3/3 < 4/2
    0/4 < 1/6 < 5/8 < 4/3 < 3/2
    0/4 < 1/8 < 2/3 < 5/6 < 3/2
    0/4 < 1/8 < 2/3 < 5/6 < 4/2
    0/4 < 1/8 < 2/3 = 4/6 < 3/2
    0/4 < 1/8 < 2/3 = 4/6 < 5/2
    0/4 < 1/8 < 2/6 < 3/2 < 5/3
    0/4 < 1/8 < 2/6 < 3/3 < 4/2
    0/4 < 1/8 < 2/6 < 3/3 < 5/2
    0/4 < 1/8 < 2/6 < 4/3 < 3/2
    0/4 < 1/8 < 2/6 < 4/3 < 5/2
    0/4 < 1/8 < 2/6 < 5/3 < 4/2
    0/4 < 1/8 < 3/6 < 2/2 < 4/3
    0/4 < 1/8 < 3/6 < 2/2 < 5/3
    0/4 < 1/8 < 3/6 < 2/3 < 4/2
    0/4 < 1/8 < 3/6 < 2/3 < 5/2
    0/4 < 1/8 < 3/6 < 4/3 < 5/2
    0/4 < 1/8 < 3/6 < 5/3 < 4/2
    0/4 < 1/8 < 4/6 < 2/2 < 5/3
    0/4 < 1/8 < 4/6 < 2/2 = 3/3
    0/4 < 1/8 < 4/6 < 3/2 < 5/3
    0/4 < 1/8 < 4/6 < 3/3 < 5/2
    0/4 < 1/8 < 5/6 < 2/2 < 4/3
    0/4 < 1/8 < 5/6 < 2/2 = 3/3
    0/4 < 1/8 < 5/6 < 3/3 < 4/2
    0/4 < 1/8 < 5/6 < 4/3 < 3/2
    0/4 < 2/6 < 1/2 < 5/8 < 3/3
    0/4 < 2/6 < 1/2 < 5/8 < 4/3
    0/4 < 2/6 < 1/2 = 4/8 < 3/3
    0/4 < 2/6 < 1/2 = 4/8 < 5/3
    0/4 < 2/6 < 3/8 < 1/2 < 4/3
    0/4 < 2/6 < 3/8 < 1/2 < 5/3
    0/4 < 2/6 < 3/8 < 4/3 < 5/2
    0/4 < 2/6 < 3/8 < 5/3 < 4/2
    0/4 < 2/6 < 4/8 < 3/2 < 5/3
    0/4 < 2/6 < 4/8 < 3/3 < 5/2
    0/4 < 2/6 < 5/8 < 3/3 < 4/2
    0/4 < 2/6 < 5/8 < 4/3 < 3/2
    0/4 < 2/8 < 1/2 < 4/6 < 3/3
    0/4 < 2/8 < 1/2 < 4/6 < 5/3
    0/4 < 2/8 < 1/2 < 5/6 < 3/3
    0/4 < 2/8 < 1/2 < 5/6 < 4/3
    0/4 < 2/8 < 1/2 = 3/6 < 4/3
    0/4 < 2/8 < 1/2 = 3/6 < 5/3
    0/4 < 2/8 < 1/3 < 3/6 < 4/2
    0/4 < 2/8 < 1/3 < 3/6 < 5/2
    0/4 < 2/8 < 1/3 < 4/6 < 3/2
    0/4 < 2/8 < 1/3 < 4/6 < 5/2
    0/4 < 2/8 < 1/3 < 5/6 < 3/2
    0/4 < 2/8 < 1/3 < 5/6 < 4/2
    0/4 < 2/8 < 3/6 < 4/3 < 5/2
    0/4 < 2/8 < 3/6 < 5/3 < 4/2
    0/4 < 2/8 < 4/6 < 3/2 < 5/3
    0/4 < 2/8 < 4/6 < 3/3 < 5/2
    0/4 < 2/8 < 5/6 < 3/3 < 4/2
    0/4 < 2/8 < 5/6 < 4/3 < 3/2
    0/4 < 3/6 < 5/8 < 2/2 < 4/3
    0/4 < 3/6 < 5/8 < 2/3 < 4/2
    0/4 < 3/6 = 4/8 < 2/2 < 5/3
    0/4 < 3/6 = 4/8 < 2/3 < 5/2
    0/4 < 3/8 < 1/2 < 2/3 < 5/6
    0/4 < 3/8 < 1/2 < 2/3 = 4/6
    0/4 < 3/8 < 1/2 < 4/6 < 5/3
    0/4 < 3/8 < 1/2 < 5/6 < 4/3
    0/4 < 3/8 < 2/3 < 5/6 < 4/2
    0/4 < 3/8 < 2/3 = 4/6 < 5/2
    0/4 < 3/8 < 4/6 < 2/2 < 5/3
    0/4 < 3/8 < 5/6 < 2/2 < 4/3
    0/4 < 4/8 < 2/3 < 5/6 < 3/2
    0/4 < 4/8 < 5/6 < 2/2 = 3/3
    0/4 < 5/8 < 2/3 = 4/6 < 3/2
    0/4 < 5/8 < 4/6 < 2/2 = 3/3
    0/6 < 1/2 < 5/8 < 2/3 < 3/4
    0/6 < 1/2 < 5/8 < 2/3 < 4/4
    0/6 < 1/2 < 5/8 < 3/3 = 4/4
    0/6 < 1/2 < 5/8 < 3/4 < 4/3
    0/6 < 1/2 = 2/4 < 5/8 < 3/3
    0/6 < 1/2 = 2/4 < 5/8 < 4/3
    0/6 < 1/2 = 2/4 = 4/8 < 3/3
    0/6 < 1/2 = 2/4 = 4/8 < 5/3
    0/6 < 1/2 = 4/8 < 2/3 < 3/4
    0/6 < 1/2 = 4/8 < 2/3 < 5/4
    0/6 < 1/2 = 4/8 < 3/3 < 5/4
    0/6 < 1/2 = 4/8 < 3/4 < 5/3
    0/6 < 1/3 < 2/4 < 5/8 < 3/2
    0/6 < 1/3 < 2/4 < 5/8 < 4/2
    0/6 < 1/3 < 2/4 = 4/8 < 3/2
    0/6 < 1/3 < 2/4 = 4/8 < 5/2
    0/6 < 1/3 < 3/8 < 2/2 < 5/4
    0/6 < 1/3 < 3/8 < 2/2 = 4/4
    0/6 < 1/3 < 3/8 < 2/4 < 4/2
    0/6 < 1/3 < 3/8 < 2/4 < 5/2
    0/6 < 1/3 < 3/8 < 4/4 < 5/2
    0/6 < 1/3 < 3/8 < 5/4 < 4/2
    0/6 < 1/3 < 4/8 < 2/2 < 5/4
    0/6 < 1/3 < 4/8 < 3/4 < 2/2
    0/6 < 1/3 < 4/8 < 3/4 < 5/2
    0/6 < 1/3 < 4/8 < 5/4 < 3/2
    0/6 < 1/3 < 5/8 < 2/2 = 4/4
    0/6 < 1/3 < 5/8 < 3/4 < 2/2
    0/6 < 1/3 < 5/8 < 3/4 < 4/2
    0/6 < 1/3 < 5/8 < 4/4 < 3/2
    0/6 < 1/4 < 3/8 < 2/2 < 4/3
    0/6 < 1/4 < 3/8 < 2/2 < 5/3
    0/6 < 1/4 < 3/8 < 2/3 < 4/2
    0/6 < 1/4 < 3/8 < 2/3 < 5/2
    0/6 < 1/4 < 3/8 < 4/3 < 5/2
    0/6 < 1/4 < 3/8 < 5/3 < 4/2
    0/6 < 1/4 < 4/8 < 2/2 < 5/3
    0/6 < 1/4 < 4/8 < 2/2 = 3/3
    0/6 < 1/4 < 4/8 < 2/3 < 3/2
    0/6 < 1/4 < 4/8 < 2/3 < 5/2
    0/6 < 1/4 < 4/8 < 3/2 < 5/3
    0/6 < 1/4 < 4/8 < 3/3 < 5/2
    0/6 < 1/4 < 5/8 < 2/2 < 4/3
    0/6 < 1/4 < 5/8 < 2/2 = 3/3
    0/6 < 1/4 < 5/8 < 2/3 < 3/2
    0/6 < 1/4 < 5/8 < 2/3 < 4/2
    0/6 < 1/4 < 5/8 < 3/3 < 4/2
    0/6 < 1/4 < 5/8 < 4/3 < 3/2
    0/6 < 1/4 = 2/8 < 3/2 < 5/3
    0/6 < 1/4 = 2/8 < 3/3 < 4/2
    0/6 < 1/4 = 2/8 < 3/3 < 5/2
    0/6 < 1/4 = 2/8 < 4/3 < 3/2
    0/6 < 1/4 = 2/8 < 4/3 < 5/2
    0/6 < 1/4 = 2/8 < 5/3 < 4/2
    0/6 < 1/8 < 2/2 < 5/4 < 4/3
    0/6 < 1/8 < 2/2 = 3/3 < 5/4
    0/6 < 1/8 < 2/2 = 3/3 = 4/4
    0/6 < 1/8 < 2/2 = 4/4 < 5/3
    0/6 < 1/8 < 2/3 < 3/4 < 4/2
    0/6 < 1/8 < 2/3 < 3/4 < 5/2
    0/6 < 1/8 < 2/3 < 4/4 < 3/2
    0/6 < 1/8 < 2/3 < 4/4 < 5/2
    0/6 < 1/8 < 2/3 < 5/4 < 3/2
    0/6 < 1/8 < 2/3 < 5/4 < 4/2
    0/6 < 1/8 < 2/4 < 3/2 < 5/3
    0/6 < 1/8 < 2/4 < 3/3 < 4/2
    0/6 < 1/8 < 2/4 < 3/3 < 5/2
    0/6 < 1/8 < 2/4 < 4/3 < 3/2
    0/6 < 1/8 < 2/4 < 4/3 < 5/2
    0/6 < 1/8 < 2/4 < 5/3 < 4/2
    0/6 < 1/8 < 3/3 < 5/4 < 4/2
    0/6 < 1/8 < 3/3 = 4/4 < 5/2
    0/6 < 1/8 < 3/4 < 2/2 < 4/3
    0/6 < 1/8 < 3/4 < 2/2 < 5/3
    0/6 < 1/8 < 3/4 < 4/3 < 5/2
    0/6 < 1/8 < 3/4 < 5/3 < 4/2
    0/6 < 1/8 < 4/4 < 3/2 < 5/3
    0/6 < 1/8 < 5/4 < 4/3 < 3/2
    0/6 < 2/4 < 5/8 < 3/3 < 4/2
    0/6 < 2/4 < 5/8 < 4/3 < 3/2
    0/6 < 2/4 = 4/8 < 3/2 < 5/3
    0/6 < 2/4 = 4/8 < 3/3 < 5/2
    0/6 < 2/8 < 1/2 < 3/3 < 5/4
    0/6 < 2/8 < 1/2 < 3/3 = 4/4
    0/6 < 2/8 < 1/2 < 3/4 < 4/3
    0/6 < 2/8 < 1/2 < 3/4 < 5/3
    0/6 < 2/8 < 1/2 < 4/4 < 5/3
    0/6 < 2/8 < 1/2 < 5/4 < 4/3
    0/6 < 2/8 < 1/3 < 3/4 < 4/2
    0/6 < 2/8 < 1/3 < 3/4 < 5/2
    0/6 < 2/8 < 1/3 < 4/4 < 3/2
    0/6 < 2/8 < 1/3 < 4/4 < 5/2
    0/6 < 2/8 < 1/3 < 5/4 < 3/2
    0/6 < 2/8 < 1/3 < 5/4 < 4/2
    0/6 < 2/8 < 3/3 < 5/4 < 4/2
    0/6 < 2/8 < 3/3 = 4/4 < 5/2
    0/6 < 2/8 < 3/4 < 4/3 < 5/2
    0/6 < 2/8 < 3/4 < 5/3 < 4/2
    0/6 < 2/8 < 4/4 < 3/2 < 5/3
    0/6 < 2/8 < 5/4 < 4/3 < 3/2
    0/6 < 3/8 < 1/2 < 2/3 < 4/4
    0/6 < 3/8 < 1/2 < 2/3 < 5/4
    0/6 < 3/8 < 1/2 < 4/4 < 5/3
    0/6 < 3/8 < 1/2 < 5/4 < 4/3
    0/6 < 3/8 < 1/2 = 2/4 < 4/3
    0/6 < 3/8 < 1/2 = 2/4 < 5/3
    0/6 < 3/8 < 2/2 < 5/4 < 4/3
    0/6 < 3/8 < 2/2 = 4/4 < 5/3
    0/6 < 3/8 < 2/3 < 4/4 < 5/2
    0/6 < 3/8 < 2/3 < 5/4 < 4/2
    0/6 < 3/8 < 2/4 < 4/3 < 5/2
    0/6 < 3/8 < 2/4 < 5/3 < 4/2
    0/6 < 4/8 < 2/2 = 3/3 < 5/4
    0/6 < 4/8 < 2/3 < 3/4 < 5/2
    0/6 < 4/8 < 2/3 < 5/4 < 3/2
    0/6 < 4/8 < 3/4 < 2/2 < 5/3
    0/6 < 5/8 < 2/2 = 3/3 = 4/4
    0/6 < 5/8 < 2/3 < 3/4 < 4/2
    0/6 < 5/8 < 2/3 < 4/4 < 3/2
    0/6 < 5/8 < 3/4 < 2/2 < 4/3
    0/8 < 1/2 < 2/3 < 3/4 < 5/6
    0/8 < 1/2 < 2/3 < 5/6 < 4/4
    0/8 < 1/2 < 2/3 = 4/6 < 3/4
    0/8 < 1/2 < 2/3 = 4/6 < 5/4
    0/8 < 1/2 < 3/4 < 5/6 < 4/3
    0/8 < 1/2 < 4/6 < 3/3 < 5/4
    0/8 < 1/2 < 4/6 < 3/4 < 5/3
    0/8 < 1/2 < 5/6 < 3/3 = 4/4
    0/8 < 1/2 = 2/4 < 4/6 < 3/3
    0/8 < 1/2 = 2/4 < 4/6 < 5/3
    0/8 < 1/2 = 2/4 < 5/6 < 3/3
    0/8 < 1/2 = 2/4 < 5/6 < 4/3
    0/8 < 1/2 = 2/4 = 3/6 < 4/3
    0/8 < 1/2 = 2/4 = 3/6 < 5/3
    0/8 < 1/2 = 3/6 < 2/3 < 4/4
    0/8 < 1/2 = 3/6 < 2/3 < 5/4
    0/8 < 1/2 = 3/6 < 4/4 < 5/3
    0/8 < 1/2 = 3/6 < 5/4 < 4/3
    0/8 < 1/3 < 2/4 < 4/6 < 3/2
    0/8 < 1/3 < 2/4 < 4/6 < 5/2
    0/8 < 1/3 < 2/4 < 5/6 < 3/2
    0/8 < 1/3 < 2/4 < 5/6 < 4/2
    0/8 < 1/3 < 2/4 = 3/6 < 4/2
    0/8 < 1/3 < 2/4 = 3/6 < 5/2
    0/8 < 1/3 < 3/4 < 5/6 < 2/2
    0/8 < 1/3 < 3/4 < 5/6 < 4/2
    0/8 < 1/3 < 3/6 < 2/2 < 5/4
    0/8 < 1/3 < 3/6 < 2/2 = 4/4
    0/8 < 1/3 < 3/6 < 4/4 < 5/2
    0/8 < 1/3 < 3/6 < 5/4 < 4/2
    0/8 < 1/3 < 4/6 < 2/2 < 5/4
    0/8 < 1/3 < 4/6 < 3/4 < 2/2
    0/8 < 1/3 < 4/6 < 3/4 < 5/2
    0/8 < 1/3 < 4/6 < 5/4 < 3/2
    0/8 < 1/3 < 5/6 < 2/2 = 4/4
    0/8 < 1/3 < 5/6 < 4/4 < 3/2
    0/8 < 1/3 = 2/6 < 3/4 < 4/2
    0/8 < 1/3 = 2/6 < 3/4 < 5/2
    0/8 < 1/3 = 2/6 < 4/4 < 3/2
    0/8 < 1/3 = 2/6 < 4/4 < 5/2
    0/8 < 1/3 = 2/6 < 5/4 < 3/2
    0/8 < 1/3 = 2/6 < 5/4 < 4/2
    0/8 < 1/4 < 2/3 < 5/6 < 3/2
    0/8 < 1/4 < 2/3 < 5/6 < 4/2
    0/8 < 1/4 < 2/3 = 4/6 < 3/2
    0/8 < 1/4 < 2/3 = 4/6 < 5/2
    0/8 < 1/4 < 2/6 < 3/2 < 5/3
    0/8 < 1/4 < 2/6 < 3/3 < 4/2
    0/8 < 1/4 < 2/6 < 3/3 < 5/2
    0/8 < 1/4 < 2/6 < 4/3 < 3/2
    0/8 < 1/4 < 2/6 < 4/3 < 5/2
    0/8 < 1/4 < 2/6 < 5/3 < 4/2
    0/8 < 1/4 < 3/6 < 2/2 < 4/3
    0/8 < 1/4 < 3/6 < 2/2 < 5/3
    0/8 < 1/4 < 3/6 < 2/3 < 4/2
    0/8 < 1/4 < 3/6 < 2/3 < 5/2
    0/8 < 1/4 < 3/6 < 4/3 < 5/2
    0/8 < 1/4 < 3/6 < 5/3 < 4/2
    0/8 < 1/4 < 4/6 < 2/2 < 5/3
    0/8 < 1/4 < 4/6 < 2/2 = 3/3
    0/8 < 1/4 < 4/6 < 3/2 < 5/3
    0/8 < 1/4 < 4/6 < 3/3 < 5/2
    0/8 < 1/4 < 5/6 < 2/2 < 4/3
    0/8 < 1/4 < 5/6 < 2/2 = 3/3
    0/8 < 1/4 < 5/6 < 3/3 < 4/2
    0/8 < 1/4 < 5/6 < 4/3 < 3/2
    0/8 < 1/6 < 2/2 < 5/4 < 4/3
    0/8 < 1/6 < 2/2 = 3/3 < 5/4
    0/8 < 1/6 < 2/2 = 3/3 = 4/4
    0/8 < 1/6 < 2/2 = 4/4 < 5/3
    0/8 < 1/6 < 2/3 < 3/4 < 4/2
    0/8 < 1/6 < 2/3 < 3/4 < 5/2
    0/8 < 1/6 < 2/3 < 4/4 < 3/2
    0/8 < 1/6 < 2/3 < 4/4 < 5/2
    0/8 < 1/6 < 2/3 < 5/4 < 3/2
    0/8 < 1/6 < 2/3 < 5/4 < 4/2
    0/8 < 1/6 < 2/4 < 3/2 < 5/3
    0/8 < 1/6 < 2/4 < 3/3 < 4/2
    0/8 < 1/6 < 2/4 < 3/3 < 5/2
    0/8 < 1/6 < 2/4 < 4/3 < 3/2
    0/8 < 1/6 < 2/4 < 4/3 < 5/2
    0/8 < 1/6 < 2/4 < 5/3 < 4/2
    0/8 < 1/6 < 3/3 < 5/4 < 4/2
    0/8 < 1/6 < 3/3 = 4/4 < 5/2
    0/8 < 1/6 < 3/4 < 2/2 < 4/3
    0/8 < 1/6 < 3/4 < 2/2 < 5/3
    0/8 < 1/6 < 3/4 < 4/3 < 5/2
    0/8 < 1/6 < 3/4 < 5/3 < 4/2
    0/8 < 1/6 < 4/4 < 3/2 < 5/3
    0/8 < 1/6 < 5/4 < 4/3 < 3/2
    0/8 < 2/3 < 3/4 < 5/6 < 4/2
    0/8 < 2/3 < 5/6 < 4/4 < 3/2
    0/8 < 2/3 = 4/6 < 3/4 < 5/2
    0/8 < 2/3 = 4/6 < 5/4 < 3/2
    0/8 < 2/4 < 4/6 < 3/2 < 5/3
    0/8 < 2/4 < 4/6 < 3/3 < 5/2
    0/8 < 2/4 < 5/6 < 3/3 < 4/2
    0/8 < 2/4 < 5/6 < 4/3 < 3/2
    0/8 < 2/4 = 3/6 < 4/3 < 5/2
    0/8 < 2/4 = 3/6 < 5/3 < 4/2
    0/8 < 2/6 < 1/2 < 3/3 < 5/4
    0/8 < 2/6 < 1/2 < 3/3 = 4/4
    0/8 < 2/6 < 1/2 < 3/4 < 4/3
    0/8 < 2/6 < 1/2 < 3/4 < 5/3
    0/8 < 2/6 < 1/2 < 4/4 < 5/3
    0/8 < 2/6 < 1/2 < 5/4 < 4/3
    0/8 < 2/6 < 3/3 < 5/4 < 4/2
    0/8 < 2/6 < 3/3 = 4/4 < 5/2
    0/8 < 2/6 < 3/4 < 4/3 < 5/2
    0/8 < 2/6 < 3/4 < 5/3 < 4/2
    0/8 < 2/6 < 4/4 < 3/2 < 5/3
    0/8 < 2/6 < 5/4 < 4/3 < 3/2
    0/8 < 3/4 < 5/6 < 2/2 < 4/3
    0/8 < 3/6 < 2/2 < 5/4 < 4/3
    0/8 < 3/6 < 2/2 = 4/4 < 5/3
    0/8 < 3/6 < 2/3 < 4/4 < 5/2
    0/8 < 3/6 < 2/3 < 5/4 < 4/2
    0/8 < 4/6 < 2/2 = 3/3 < 5/4
    0/8 < 4/6 < 3/4 < 2/2 < 5/3
    0/8 < 5/6 < 2/2 = 3/3 = 4/4
    1/2 < 5/8 < 2/3 = 4/6 < 3/4
    1/2 = 2/4 < 5/8 < 4/6 < 3/3
    1/2 = 2/4 = 3/6 < 5/8 < 4/3
    1/2 = 2/4 = 3/6 = 4/8 < 5/3
    1/2 = 2/4 = 4/8 < 5/6 < 3/3
    1/2 = 3/6 < 5/8 < 2/3 < 4/4
    1/2 = 3/6 = 4/8 < 2/3 < 5/4
    1/2 = 4/8 < 2/3 < 3/4 < 5/6
    1/3 < 2/4 < 5/8 < 4/6 < 3/2
    1/3 < 2/4 = 3/6 < 5/8 < 4/2
    1/3 < 2/4 = 3/6 = 4/8 < 5/2
    1/3 < 2/4 = 4/8 < 5/6 < 3/2
    1/3 < 3/6 < 5/8 < 2/2 = 4/4
    1/3 < 3/6 = 4/8 < 2/2 < 5/4
    1/3 < 3/8 < 2/4 < 4/6 < 5/2
    1/3 < 3/8 < 2/4 < 5/6 < 4/2
    1/3 < 3/8 < 4/6 < 2/2 < 5/4
    1/3 < 3/8 < 5/6 < 2/2 = 4/4
    1/3 < 4/8 < 3/4 < 5/6 < 2/2
    1/3 < 5/8 < 4/6 < 3/4 < 2/2
    1/3 = 2/6 < 3/8 < 4/4 < 5/2
    1/3 = 2/6 < 3/8 < 5/4 < 4/2
    1/3 = 2/6 < 4/8 < 3/4 < 5/2
    1/3 = 2/6 < 4/8 < 5/4 < 3/2
    1/3 = 2/6 < 5/8 < 3/4 < 4/2
    1/3 = 2/6 < 5/8 < 4/4 < 3/2
    1/4 < 2/6 < 3/8 < 4/3 < 5/2
    1/4 < 2/6 < 3/8 < 5/3 < 4/2
    1/4 < 2/6 < 4/8 < 3/2 < 5/3
    1/4 < 2/6 < 4/8 < 3/3 < 5/2
    1/4 < 2/6 < 5/8 < 3/3 < 4/2
    1/4 < 2/6 < 5/8 < 4/3 < 3/2
    1/4 < 3/6 < 5/8 < 2/2 < 4/3
    1/4 < 3/6 < 5/8 < 2/3 < 4/2
    1/4 < 3/6 = 4/8 < 2/2 < 5/3
    1/4 < 3/6 = 4/8 < 2/3 < 5/2
    1/4 < 3/8 < 2/3 < 5/6 < 4/2
    1/4 < 3/8 < 2/3 = 4/6 < 5/2
    1/4 < 3/8 < 4/6 < 2/2 < 5/3
    1/4 < 3/8 < 5/6 < 2/2 < 4/3
    1/4 < 4/8 < 2/3 < 5/6 < 3/2
    1/4 < 4/8 < 5/6 < 2/2 = 3/3
    1/4 < 5/8 < 2/3 = 4/6 < 3/2
    1/4 < 5/8 < 4/6 < 2/2 = 3/3
    1/4 = 2/8 < 3/6 < 4/3 < 5/2
    1/4 = 2/8 < 3/6 < 5/3 < 4/2
    1/4 = 2/8 < 4/6 < 3/2 < 5/3
    1/4 = 2/8 < 4/6 < 3/3 < 5/2
    1/4 = 2/8 < 5/6 < 3/3 < 4/2
    1/4 = 2/8 < 5/6 < 4/3 < 3/2
    1/6 < 2/4 < 5/8 < 3/3 < 4/2
    1/6 < 2/4 < 5/8 < 4/3 < 3/2
    1/6 < 2/4 = 4/8 < 3/2 < 5/3
    1/6 < 2/4 = 4/8 < 3/3 < 5/2
    1/6 < 2/8 < 3/3 < 5/4 < 4/2
    1/6 < 2/8 < 3/3 = 4/4 < 5/2
    1/6 < 2/8 < 3/4 < 4/3 < 5/2
    1/6 < 2/8 < 3/4 < 5/3 < 4/2
    1/6 < 2/8 < 4/4 < 3/2 < 5/3
    1/6 < 2/8 < 5/4 < 4/3 < 3/2
    1/6 < 3/8 < 2/2 < 5/4 < 4/3
    1/6 < 3/8 < 2/2 = 4/4 < 5/3
    1/6 < 3/8 < 2/3 < 4/4 < 5/2
    1/6 < 3/8 < 2/3 < 5/4 < 4/2
    1/6 < 3/8 < 2/4 < 4/3 < 5/2
    1/6 < 3/8 < 2/4 < 5/3 < 4/2
    1/6 < 4/8 < 2/2 = 3/3 < 5/4
    1/6 < 4/8 < 2/3 < 3/4 < 5/2
    1/6 < 4/8 < 2/3 < 5/4 < 3/2
    1/6 < 4/8 < 3/4 < 2/2 < 5/3
    1/6 < 5/8 < 2/2 = 3/3 = 4/4
    1/6 < 5/8 < 2/3 < 3/4 < 4/2
    1/6 < 5/8 < 2/3 < 4/4 < 3/2
    1/6 < 5/8 < 3/4 < 2/2 < 4/3
    1/8 < 2/3 < 3/4 < 5/6 < 4/2
    1/8 < 2/3 < 5/6 < 4/4 < 3/2
    1/8 < 2/3 = 4/6 < 3/4 < 5/2
    1/8 < 2/3 = 4/6 < 5/4 < 3/2
    1/8 < 2/4 < 4/6 < 3/2 < 5/3
    1/8 < 2/4 < 4/6 < 3/3 < 5/2
    1/8 < 2/4 < 5/6 < 3/3 < 4/2
    1/8 < 2/4 < 5/6 < 4/3 < 3/2
    1/8 < 2/4 = 3/6 < 4/3 < 5/2
    1/8 < 2/4 = 3/6 < 5/3 < 4/2
    1/8 < 2/6 < 3/3 < 5/4 < 4/2
    1/8 < 2/6 < 3/3 = 4/4 < 5/2
    1/8 < 2/6 < 3/4 < 4/3 < 5/2
    1/8 < 2/6 < 3/4 < 5/3 < 4/2
    1/8 < 2/6 < 4/4 < 3/2 < 5/3
    1/8 < 2/6 < 5/4 < 4/3 < 3/2
    1/8 < 3/4 < 5/6 < 2/2 < 4/3
    1/8 < 3/6 < 2/2 < 5/4 < 4/3
    1/8 < 3/6 < 2/2 = 4/4 < 5/3
    1/8 < 3/6 < 2/3 < 4/4 < 5/2
    1/8 < 3/6 < 2/3 < 5/4 < 4/2
    1/8 < 4/6 < 2/2 = 3/3 < 5/4
    1/8 < 4/6 < 3/4 < 2/2 < 5/3
    1/8 < 5/6 < 2/2 = 3/3 = 4/4
    2/6 < 1/2 < 5/8 < 3/3 = 4/4
    2/6 < 1/2 < 5/8 < 3/4 < 4/3
    2/6 < 1/2 = 4/8 < 3/3 < 5/4
    2/6 < 1/2 = 4/8 < 3/4 < 5/3
    2/6 < 3/8 < 1/2 < 4/4 < 5/3
    2/6 < 3/8 < 1/2 < 5/4 < 4/3
    2/8 < 1/2 < 3/4 < 5/6 < 4/3
    2/8 < 1/2 < 4/6 < 3/3 < 5/4
    2/8 < 1/2 < 4/6 < 3/4 < 5/3
    2/8 < 1/2 < 5/6 < 3/3 = 4/4
    2/8 < 1/2 = 3/6 < 4/4 < 5/3
    2/8 < 1/2 = 3/6 < 5/4 < 4/3
    2/8 < 1/3 < 3/4 < 5/6 < 4/2
    2/8 < 1/3 < 3/6 < 4/4 < 5/2
    2/8 < 1/3 < 3/6 < 5/4 < 4/2
    2/8 < 1/3 < 4/6 < 3/4 < 5/2
    2/8 < 1/3 < 4/6 < 5/4 < 3/2
    2/8 < 1/3 < 5/6 < 4/4 < 3/2
    3/8 < 1/2 < 2/3 < 5/6 < 4/4
    3/8 < 1/2 < 2/3 = 4/6 < 5/4
    3/8 < 1/2 = 2/4 < 4/6 < 5/3
    3/8 < 1/2 = 2/4 < 5/6 < 4/3

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