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Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a true statement. Try to find solutions where the fractions are in their lowest terms.
Hint
Try creating the mixed number first.
Answer
There are multiple answers… 4/3 > 1+2/9 > 7/8> 5/6, 9/1>2 3/4>7/8>5/6, etc.
Source: Charlotte Hawthorne
There are 456 solutions where the whole part of the mixed number is not 0 and each fraction is in its simplest form (including no 1 in the denominator):
3/2 > 1 4/9 > 6/5 > 7/8
3/2 > 1 4/9 > 6/5 > 8/7
3/2 > 1 4/9 > 6/7 > 5/8
3/2 > 1 4/9 > 7/6 > 5/8
3/2 > 1 4/9 > 7/8 > 5/6
3/2 > 1 4/9 > 8/7 > 5/6
4/3 > 1 2/7 > 6/5 > 8/9
4/3 > 1 2/7 > 6/5 > 9/8
4/3 > 1 2/7 > 8/9 > 5/6
4/3 > 1 2/7 > 9/8 > 5/6
4/3 > 1 2/9 > 6/5 > 7/8
4/3 > 1 2/9 > 6/5 > 8/7
4/3 > 1 2/9 > 6/7 > 5/8
4/3 > 1 2/9 > 7/6 > 5/8
4/3 > 1 2/9 > 7/8 > 5/6
4/3 > 1 2/9 > 8/7 > 5/6
5/2 > 1 3/4 > 7/6 > 8/9
5/2 > 1 3/4 > 7/6 > 9/8
5/2 > 1 3/4 > 8/9 > 6/7
5/2 > 1 3/4 > 9/8 > 6/7
5/2 > 1 3/8 > 6/7 > 4/9
5/2 > 1 3/8 > 7/6 > 4/9
5/2 > 1 4/3 > 7/6 > 8/9
5/2 > 1 4/3 > 7/6 > 9/8
5/2 > 1 4/3 > 8/9 > 6/7
5/2 > 1 4/3 > 9/8 > 6/7
5/2 > 1 4/9 > 6/7 > 3/8
5/2 > 1 4/9 > 7/6 > 3/8
5/2 > 1 6/7 > 4/3 > 8/9
5/2 > 1 6/7 > 4/3 > 9/8
5/2 > 1 6/7 > 4/9 > 3/8
5/2 > 1 6/7 > 8/9 > 3/4
5/2 > 1 6/7 > 9/8 > 3/4
5/2 > 1 7/6 > 4/3 > 8/9
5/2 > 1 7/6 > 4/3 > 9/8
5/2 > 1 7/6 > 4/9 > 3/8
5/2 > 1 7/6 > 8/9 > 3/4
5/2 > 1 7/6 > 9/8 > 3/4
5/2 > 1 8/9 > 4/3 > 6/7
5/2 > 1 8/9 > 4/3 > 7/6
5/2 > 1 8/9 > 6/7 > 3/4
5/2 > 1 8/9 > 7/6 > 3/4
5/2 > 1 9/8 > 4/3 > 6/7
5/2 > 1 9/8 > 4/3 > 7/6
5/2 > 1 9/8 > 6/7 > 3/4
5/2 > 1 9/8 > 7/6 > 3/4
5/4 > 1 2/9 > 6/7 > 3/8
5/4 > 1 2/9 > 7/6 > 3/8
7/2 > 1 3/4 > 6/5 > 8/9
7/2 > 1 3/4 > 6/5 > 9/8
7/2 > 1 3/4 > 8/9 > 5/6
7/2 > 1 3/4 > 9/8 > 5/6
7/2 > 1 3/8 > 5/6 > 4/9
7/2 > 1 3/8 > 6/5 > 4/9
7/2 > 1 4/3 > 6/5 > 8/9
7/2 > 1 4/3 > 6/5 > 9/8
7/2 > 1 4/3 > 8/9 > 5/6
7/2 > 1 4/3 > 9/8 > 5/6
7/2 > 1 4/9 > 5/6 > 3/8
7/2 > 1 4/9 > 6/5 > 3/8
7/2 > 1 5/6 > 4/3 > 8/9
7/2 > 1 5/6 > 4/3 > 9/8
7/2 > 1 5/6 > 4/9 > 3/8
7/2 > 1 5/6 > 8/9 > 3/4
7/2 > 1 5/6 > 9/8 > 3/4
7/2 > 1 6/5 > 4/3 > 8/9
7/2 > 1 6/5 > 4/3 > 9/8
7/2 > 1 6/5 > 4/9 > 3/8
7/2 > 1 6/5 > 8/9 > 3/4
7/2 > 1 6/5 > 9/8 > 3/4
7/2 > 1 8/9 > 4/3 > 5/6
7/2 > 1 8/9 > 4/3 > 6/5
7/2 > 1 8/9 > 5/6 > 3/4
7/2 > 1 8/9 > 6/5 > 3/4
7/2 > 1 9/4 > 5/6 > 3/8
7/2 > 1 9/4 > 6/5 > 3/8
7/2 > 1 9/4 > 8/3 > 5/6
7/2 > 1 9/4 > 8/3 > 6/5
7/2 > 1 9/8 > 4/3 > 5/6
7/2 > 1 9/8 > 4/3 > 6/5
7/2 > 1 9/8 > 5/6 > 3/4
7/2 > 1 9/8 > 6/5 > 3/4
7/2 > 3 1/4 > 6/5 > 8/9
7/2 > 3 1/4 > 6/5 > 9/8
7/2 > 3 1/4 > 8/9 > 5/6
7/2 > 3 1/4 > 9/8 > 5/6
7/2 > 3 1/6 > 5/4 > 8/9
7/2 > 3 1/6 > 5/4 > 9/8
7/2 > 3 1/6 > 5/8 > 4/9
7/2 > 3 1/6 > 8/5 > 4/9
7/2 > 3 1/6 > 8/9 > 4/5
7/2 > 3 1/6 > 9/4 > 5/8
7/2 > 3 1/6 > 9/4 > 8/5
7/2 > 3 1/6 > 9/8 > 4/5
7/2 > 3 1/8 > 5/6 > 4/9
7/2 > 3 1/8 > 6/5 > 4/9
7/2 > 3 1/8 > 9/4 > 5/6
7/2 > 3 1/8 > 9/4 > 6/5
7/2 > 3 4/9 > 5/6 > 1/8
7/2 > 3 4/9 > 5/8 > 1/6
7/2 > 3 4/9 > 6/5 > 1/8
7/2 > 3 4/9 > 8/5 > 1/6
7/3 > 2 1/4 > 6/5 > 8/9
7/3 > 2 1/4 > 6/5 > 9/8
7/3 > 2 1/4 > 8/9 > 5/6
7/3 > 2 1/4 > 9/8 > 5/6
7/3 > 2 1/6 > 5/4 > 8/9
7/3 > 2 1/6 > 5/4 > 9/8
7/3 > 2 1/6 > 5/8 > 4/9
7/3 > 2 1/6 > 8/5 > 4/9
7/3 > 2 1/6 > 8/9 > 4/5
7/3 > 2 1/6 > 9/8 > 4/5
7/3 > 2 1/8 > 5/6 > 4/9
7/3 > 2 1/8 > 6/5 > 4/9
7/4 > 1 2/3 > 6/5 > 8/9
7/4 > 1 2/3 > 6/5 > 9/8
7/4 > 1 2/3 > 8/9 > 5/6
7/4 > 1 2/3 > 9/8 > 5/6
7/4 > 1 2/9 > 5/6 > 3/8
7/4 > 1 2/9 > 6/5 > 3/8
7/4 > 1 3/8 > 5/6 > 2/9
7/4 > 1 3/8 > 6/5 > 2/9
8/3 > 1 2/5 > 6/7 > 4/9
8/3 > 1 2/5 > 7/6 > 4/9
8/3 > 1 2/7 > 5/6 > 4/9
8/3 > 1 2/7 > 6/5 > 4/9
8/3 > 1 2/9 > 5/6 > 4/7
8/3 > 1 2/9 > 6/5 > 4/7
8/3 > 1 2/9 > 6/7 > 4/5
8/3 > 1 2/9 > 7/6 > 4/5
8/3 > 1 4/5 > 6/7 > 2/9
8/3 > 1 4/5 > 7/6 > 2/9
8/3 > 1 4/7 > 5/6 > 2/9
8/3 > 1 4/7 > 6/5 > 2/9
8/3 > 1 4/9 > 5/6 > 2/7
8/3 > 1 4/9 > 6/5 > 2/7
8/3 > 1 4/9 > 6/7 > 2/5
8/3 > 1 4/9 > 7/6 > 2/5
8/3 > 1 5/4 > 6/7 > 2/9
8/3 > 1 5/4 > 7/6 > 2/9
8/3 > 1 5/6 > 4/7 > 2/9
8/3 > 1 5/6 > 4/9 > 2/7
8/3 > 1 5/6 > 7/4 > 2/9
8/3 > 1 6/5 > 4/7 > 2/9
8/3 > 1 6/5 > 4/9 > 2/7
8/3 > 1 6/5 > 7/4 > 2/9
8/3 > 1 6/7 > 4/5 > 2/9
8/3 > 1 6/7 > 4/9 > 2/5
8/3 > 1 6/7 > 5/4 > 2/9
8/3 > 1 7/6 > 4/5 > 2/9
8/3 > 1 7/6 > 4/9 > 2/5
8/3 > 1 7/6 > 5/4 > 2/9
8/3 > 2 1/4 > 5/6 > 7/9
8/3 > 2 1/4 > 6/5 > 7/9
8/3 > 2 1/4 > 6/7 > 5/9
8/3 > 2 1/4 > 7/6 > 5/9
8/3 > 2 1/4 > 9/5 > 6/7
8/3 > 2 1/4 > 9/5 > 7/6
8/3 > 2 1/4 > 9/7 > 5/6
8/3 > 2 1/4 > 9/7 > 6/5
8/3 > 2 1/5 > 6/7 > 4/9
8/3 > 2 1/5 > 7/6 > 4/9
8/3 > 2 1/6 > 4/5 > 7/9
8/3 > 2 1/6 > 4/7 > 5/9
8/3 > 2 1/6 > 5/4 > 7/9
8/3 > 2 1/6 > 5/7 > 4/9
8/3 > 2 1/6 > 7/4 > 5/9
8/3 > 2 1/6 > 7/5 > 4/9
8/3 > 2 1/6 > 9/5 > 4/7
8/3 > 2 1/6 > 9/5 > 7/4
8/3 > 2 1/6 > 9/7 > 4/5
8/3 > 2 1/6 > 9/7 > 5/4
8/3 > 2 1/7 > 5/6 > 4/9
8/3 > 2 1/7 > 6/5 > 4/9
8/3 > 2 1/9 > 5/4 > 6/7
8/3 > 2 1/9 > 5/4 > 7/6
8/3 > 2 1/9 > 5/6 > 4/7
8/3 > 2 1/9 > 6/5 > 4/7
8/3 > 2 1/9 > 6/7 > 4/5
8/3 > 2 1/9 > 7/4 > 5/6
8/3 > 2 1/9 > 7/4 > 6/5
8/3 > 2 1/9 > 7/6 > 4/5
8/3 > 2 4/7 > 5/6 > 1/9
8/3 > 2 4/7 > 5/9 > 1/6
8/3 > 2 4/7 > 6/5 > 1/9
8/3 > 2 4/7 > 9/5 > 1/6
8/3 > 2 4/9 > 5/6 > 1/7
8/3 > 2 4/9 > 5/7 > 1/6
8/3 > 2 4/9 > 6/5 > 1/7
8/3 > 2 4/9 > 6/7 > 1/5
8/3 > 2 4/9 > 7/5 > 1/6
8/3 > 2 4/9 > 7/6 > 1/5
8/3 > 2 5/9 > 4/7 > 1/6
8/3 > 2 5/9 > 6/7 > 1/4
8/3 > 2 5/9 > 7/4 > 1/6
8/3 > 2 5/9 > 7/6 > 1/4
8/5 > 1 2/9 > 6/7 > 3/4
8/5 > 1 2/9 > 7/6 > 3/4
8/5 > 1 4/9 > 6/7 > 2/3
8/5 > 1 4/9 > 7/6 > 2/3
9/2 > 1 3/4 > 6/5 > 7/8
9/2 > 1 3/4 > 6/5 > 8/7
9/2 > 1 3/4 > 6/7 > 5/8
9/2 > 1 3/4 > 7/6 > 5/8
9/2 > 1 3/4 > 7/8 > 5/6
9/2 > 1 3/4 > 8/5 > 6/7
9/2 > 1 3/4 > 8/5 > 7/6
9/2 > 1 3/4 > 8/7 > 5/6
9/2 > 1 3/8 > 5/4 > 6/7
9/2 > 1 3/8 > 5/4 > 7/6
9/2 > 1 3/8 > 5/6 > 4/7
9/2 > 1 3/8 > 6/5 > 4/7
9/2 > 1 3/8 > 6/7 > 4/5
9/2 > 1 3/8 > 7/6 > 4/5
9/2 > 1 4/3 > 6/5 > 7/8
9/2 > 1 4/3 > 6/5 > 8/7
9/2 > 1 4/3 > 6/7 > 5/8
9/2 > 1 4/3 > 7/6 > 5/8
9/2 > 1 4/3 > 7/8 > 5/6
9/2 > 1 4/3 > 8/5 > 6/7
9/2 > 1 4/3 > 8/5 > 7/6
9/2 > 1 4/3 > 8/7 > 5/6
9/2 > 1 4/5 > 6/7 > 3/8
9/2 > 1 4/5 > 7/6 > 3/8
9/2 > 1 4/7 > 5/6 > 3/8
9/2 > 1 4/7 > 6/5 > 3/8
9/2 > 1 5/4 > 6/7 > 3/8
9/2 > 1 5/4 > 7/6 > 3/8
9/2 > 1 5/6 > 4/3 > 7/8
9/2 > 1 5/6 > 4/3 > 8/7
9/2 > 1 5/6 > 4/7 > 3/8
9/2 > 1 5/6 > 7/4 > 3/8
9/2 > 1 5/6 > 7/8 > 3/4
9/2 > 1 5/6 > 8/7 > 3/4
9/2 > 1 5/8 > 4/3 > 6/7
9/2 > 1 5/8 > 4/3 > 7/6
9/2 > 1 5/8 > 6/7 > 3/4
9/2 > 1 5/8 > 7/6 > 3/4
9/2 > 1 6/5 > 4/3 > 7/8
9/2 > 1 6/5 > 4/3 > 8/7
9/2 > 1 6/5 > 4/7 > 3/8
9/2 > 1 6/5 > 7/4 > 3/8
9/2 > 1 6/5 > 7/8 > 3/4
9/2 > 1 6/5 > 8/7 > 3/4
9/2 > 1 6/7 > 3/4 > 5/8
9/2 > 1 6/7 > 4/3 > 5/8
9/2 > 1 6/7 > 4/5 > 3/8
9/2 > 1 6/7 > 5/4 > 3/8
9/2 > 1 6/7 > 8/5 > 3/4
9/2 > 1 6/7 > 8/5 > 4/3
9/2 > 1 7/4 > 5/6 > 3/8
9/2 > 1 7/4 > 6/5 > 3/8
9/2 > 1 7/4 > 8/3 > 5/6
9/2 > 1 7/4 > 8/3 > 6/5
9/2 > 1 7/6 > 3/4 > 5/8
9/2 > 1 7/6 > 4/3 > 5/8
9/2 > 1 7/6 > 4/5 > 3/8
9/2 > 1 7/6 > 5/4 > 3/8
9/2 > 1 7/6 > 8/5 > 3/4
9/2 > 1 7/6 > 8/5 > 4/3
9/2 > 1 7/8 > 4/3 > 5/6
9/2 > 1 7/8 > 4/3 > 6/5
9/2 > 1 7/8 > 5/6 > 3/4
9/2 > 1 7/8 > 6/5 > 3/4
9/2 > 1 8/3 > 5/4 > 6/7
9/2 > 1 8/3 > 5/4 > 7/6
9/2 > 1 8/3 > 5/6 > 4/7
9/2 > 1 8/3 > 6/5 > 4/7
9/2 > 1 8/3 > 6/7 > 4/5
9/2 > 1 8/3 > 7/4 > 5/6
9/2 > 1 8/3 > 7/4 > 6/5
9/2 > 1 8/3 > 7/6 > 4/5
9/2 > 1 8/5 > 4/3 > 6/7
9/2 > 1 8/5 > 4/3 > 7/6
9/2 > 1 8/5 > 6/7 > 3/4
9/2 > 1 8/5 > 7/6 > 3/4
9/2 > 1 8/7 > 4/3 > 5/6
9/2 > 1 8/7 > 4/3 > 6/5
9/2 > 1 8/7 > 5/6 > 3/4
9/2 > 1 8/7 > 6/5 > 3/4
9/2 > 3 1/4 > 6/5 > 7/8
9/2 > 3 1/4 > 6/5 > 8/7
9/2 > 3 1/4 > 6/7 > 5/8
9/2 > 3 1/4 > 7/6 > 5/8
9/2 > 3 1/4 > 7/8 > 5/6
9/2 > 3 1/4 > 8/5 > 6/7
9/2 > 3 1/4 > 8/5 > 7/6
9/2 > 3 1/4 > 8/7 > 5/6
9/2 > 3 1/6 > 5/4 > 7/8
9/2 > 3 1/6 > 5/4 > 8/7
9/2 > 3 1/6 > 5/8 > 4/7
9/2 > 3 1/6 > 7/4 > 5/8
9/2 > 3 1/6 > 7/4 > 8/5
9/2 > 3 1/6 > 7/8 > 4/5
9/2 > 3 1/6 > 8/5 > 4/7
9/2 > 3 1/6 > 8/7 > 4/5
9/2 > 3 1/8 > 5/4 > 6/7
9/2 > 3 1/8 > 5/4 > 7/6
9/2 > 3 1/8 > 5/6 > 4/7
9/2 > 3 1/8 > 6/5 > 4/7
9/2 > 3 1/8 > 6/7 > 4/5
9/2 > 3 1/8 > 7/4 > 5/6
9/2 > 3 1/8 > 7/4 > 6/5
9/2 > 3 1/8 > 7/6 > 4/5
9/2 > 3 4/5 > 6/7 > 1/8
9/2 > 3 4/5 > 7/6 > 1/8
9/2 > 3 4/5 > 7/8 > 1/6
9/2 > 3 4/5 > 8/7 > 1/6
9/2 > 3 4/7 > 5/6 > 1/8
9/2 > 3 4/7 > 5/8 > 1/6
9/2 > 3 4/7 > 6/5 > 1/8
9/2 > 3 4/7 > 8/5 > 1/6
9/2 > 3 5/4 > 6/7 > 1/8
9/2 > 3 5/4 > 7/6 > 1/8
9/2 > 3 5/4 > 7/8 > 1/6
9/2 > 3 5/4 > 8/7 > 1/6
9/2 > 3 5/6 > 4/7 > 1/8
9/2 > 3 5/6 > 7/4 > 1/8
9/2 > 3 5/6 > 7/8 > 1/4
9/2 > 3 5/6 > 8/7 > 1/4
9/2 > 3 5/8 > 4/7 > 1/6
9/2 > 3 5/8 > 6/7 > 1/4
9/2 > 3 5/8 > 7/4 > 1/6
9/2 > 3 5/8 > 7/6 > 1/4
9/2 > 3 6/5 > 4/7 > 1/8
9/2 > 3 6/5 > 7/4 > 1/8
9/2 > 3 6/5 > 7/8 > 1/4
9/2 > 3 6/5 > 8/7 > 1/4
9/2 > 3 6/7 > 4/5 > 1/8
9/2 > 3 6/7 > 5/4 > 1/8
9/2 > 3 6/7 > 5/8 > 1/4
9/2 > 3 6/7 > 8/5 > 1/4
9/2 > 3 7/6 > 4/5 > 1/8
9/2 > 3 7/6 > 5/4 > 1/8
9/2 > 3 7/6 > 5/8 > 1/4
9/2 > 3 7/6 > 8/5 > 1/4
9/2 > 3 7/8 > 4/5 > 1/6
9/2 > 3 7/8 > 5/4 > 1/6
9/2 > 3 7/8 > 5/6 > 1/4
9/2 > 3 7/8 > 6/5 > 1/4
9/2 > 3 8/7 > 4/5 > 1/6
9/2 > 3 8/7 > 5/4 > 1/6
9/2 > 3 8/7 > 5/6 > 1/4
9/2 > 3 8/7 > 6/5 > 1/4
9/2 > 4 1/3 > 6/5 > 7/8
9/2 > 4 1/3 > 6/5 > 8/7
9/2 > 4 1/3 > 6/7 > 5/8
9/2 > 4 1/3 > 7/6 > 5/8
9/2 > 4 1/3 > 7/8 > 5/6
9/2 > 4 1/3 > 8/5 > 6/7
9/2 > 4 1/3 > 8/5 > 7/6
9/2 > 4 1/3 > 8/7 > 5/6
9/2 > 4 1/5 > 6/7 > 3/8
9/2 > 4 1/5 > 7/6 > 3/8
9/2 > 4 1/5 > 8/3 > 6/7
9/2 > 4 1/5 > 8/3 > 7/6
9/2 > 4 1/6 > 5/3 > 7/8
9/2 > 4 1/6 > 5/3 > 8/7
9/2 > 4 1/6 > 5/7 > 3/8
9/2 > 4 1/6 > 5/8 > 3/7
9/2 > 4 1/6 > 7/3 > 5/8
9/2 > 4 1/6 > 7/3 > 8/5
9/2 > 4 1/6 > 7/5 > 3/8
9/2 > 4 1/6 > 7/8 > 3/5
9/2 > 4 1/6 > 8/3 > 5/7
9/2 > 4 1/6 > 8/3 > 7/5
9/2 > 4 1/6 > 8/5 > 3/7
9/2 > 4 1/6 > 8/7 > 3/5
9/2 > 4 1/7 > 5/6 > 3/8
9/2 > 4 1/7 > 6/5 > 3/8
9/2 > 4 1/7 > 8/3 > 5/6
9/2 > 4 1/7 > 8/3 > 6/5
9/2 > 4 1/8 > 5/3 > 6/7
9/2 > 4 1/8 > 5/3 > 7/6
9/2 > 4 1/8 > 5/6 > 3/7
9/2 > 4 1/8 > 6/5 > 3/7
9/2 > 4 1/8 > 6/7 > 3/5
9/2 > 4 1/8 > 7/3 > 5/6
9/2 > 4 1/8 > 7/3 > 6/5
9/2 > 4 1/8 > 7/6 > 3/5
9/2 > 4 3/7 > 5/6 > 1/8
9/2 > 4 3/7 > 5/8 > 1/6
9/2 > 4 3/7 > 6/5 > 1/8
9/2 > 4 3/7 > 8/5 > 1/6
9/2 > 4 3/8 > 5/6 > 1/7
9/2 > 4 3/8 > 5/7 > 1/6
9/2 > 4 3/8 > 6/5 > 1/7
9/2 > 4 3/8 > 6/7 > 1/5
9/2 > 4 3/8 > 7/5 > 1/6
9/2 > 4 3/8 > 7/6 > 1/5
9/4 > 1 2/3 > 6/5 > 7/8
9/4 > 1 2/3 > 6/5 > 8/7
9/4 > 1 2/3 > 6/7 > 5/8
9/4 > 1 2/3 > 7/6 > 5/8
9/4 > 1 2/3 > 7/8 > 5/6
9/4 > 1 2/3 > 8/5 > 6/7
9/4 > 1 2/3 > 8/5 > 7/6
9/4 > 1 2/3 > 8/7 > 5/6
9/4 > 1 2/5 > 6/7 > 3/8
9/4 > 1 2/5 > 7/6 > 3/8
9/4 > 1 2/7 > 5/6 > 3/8
9/4 > 1 2/7 > 6/5 > 3/8
9/4 > 1 3/8 > 5/6 > 2/7
9/4 > 1 3/8 > 6/5 > 2/7
9/4 > 1 3/8 > 6/7 > 2/5
9/4 > 1 3/8 > 7/6 > 2/5
9/4 > 1 5/6 > 3/2 > 7/8
9/4 > 1 5/6 > 3/2 > 8/7
9/4 > 1 5/6 > 3/8 > 2/7
9/4 > 1 5/6 > 7/8 > 2/3
9/4 > 1 5/6 > 8/7 > 2/3
9/4 > 1 5/8 > 3/2 > 6/7
9/4 > 1 5/8 > 3/2 > 7/6
9/4 > 1 5/8 > 6/7 > 2/3
9/4 > 1 5/8 > 7/6 > 2/3
9/4 > 1 6/5 > 3/2 > 7/8
9/4 > 1 6/5 > 3/2 > 8/7
9/4 > 1 6/5 > 3/8 > 2/7
9/4 > 1 6/5 > 7/8 > 2/3
9/4 > 1 6/5 > 8/7 > 2/3
9/4 > 1 6/7 > 2/3 > 5/8
9/4 > 1 6/7 > 2/5 > 3/8
9/4 > 1 6/7 > 3/2 > 5/8
9/4 > 1 6/7 > 8/5 > 2/3
9/4 > 1 6/7 > 8/5 > 3/2
9/4 > 1 7/6 > 2/3 > 5/8
9/4 > 1 7/6 > 2/5 > 3/8
9/4 > 1 7/6 > 3/2 > 5/8
9/4 > 1 7/6 > 8/5 > 2/3
9/4 > 1 7/6 > 8/5 > 3/2
9/4 > 1 7/8 > 3/2 > 5/6
9/4 > 1 7/8 > 3/2 > 6/5
9/4 > 1 7/8 > 5/6 > 2/3
9/4 > 1 7/8 > 6/5 > 2/3
9/4 > 1 8/7 > 3/2 > 5/6
9/4 > 1 8/7 > 3/2 > 6/5
9/4 > 1 8/7 > 5/6 > 2/3
9/4 > 1 8/7 > 6/5 > 2/3
9/4 > 2 1/5 > 6/7 > 3/8
9/4 > 2 1/5 > 7/6 > 3/8
9/4 > 2 1/6 > 5/3 > 7/8
9/4 > 2 1/6 > 5/3 > 8/7
9/4 > 2 1/6 > 5/7 > 3/8
9/4 > 2 1/6 > 5/8 > 3/7
9/4 > 2 1/6 > 7/5 > 3/8
9/4 > 2 1/6 > 7/8 > 3/5
9/4 > 2 1/6 > 8/5 > 3/7
9/4 > 2 1/6 > 8/7 > 3/5
9/4 > 2 1/7 > 5/6 > 3/8
9/4 > 2 1/7 > 6/5 > 3/8
9/4 > 2 1/8 > 5/3 > 6/7
9/4 > 2 1/8 > 5/3 > 7/6
9/4 > 2 1/8 > 5/6 > 3/7
9/4 > 2 1/8 > 6/5 > 3/7
9/4 > 2 1/8 > 6/7 > 3/5
9/4 > 2 1/8 > 7/6 > 3/5
As you can see, due to the mixed number, it’s not possible for the first fraction to be a proper fraction.
If you allow 1 in the denominator, there are another 1,908 solutions.
If you additionally allow fractions that are not in their lowest forms, there are another 8,243 solutions on top of 1,908+456 solutions.
9/1 >2 3/4 > 7/8 >5/6