Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create two different fractions: one that is less than one half and one that is more than one half.
Hint
How can we tell when a fraction is less than one half?
How can we find a fraction that is less than one half but has a numerator larger than 1?
How can we tell when a fraction is more than one half?
How can we find a fraction that is less than one half but has a numerator larger than 1?
How can we tell when a fraction is more than one half?
Answer
There are many possible answers including
1/4 and 8/9
Other answers you may not expect would be improper fractions that are greater than 1/2 such as 5/2.
Source: Robert Kaplinsky
1/5 and 7/8
i agree with you
1/8 and 3/4
4/2 and 2/2
It could be 1/41/2.
Sorry, there was a glitch. I meant to say that 1/4 is less than 1/2 and 3/4 is greater than 1/2.
There are 502 solutions (166 of which are proper fractions, with 107 of them only containing fractions in their simplest form):
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/3 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/4 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/5 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/6 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/7 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/8 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
1/9 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/5 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/6 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/7 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/8 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
2/9 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/7 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/8 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
3/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
4/9 1/2
Somehow, this comment glitched and I can’t edit it or post the corrected answer…
1/4 1/2
13/40 and 17/30