Open Middle®
Directions: Use the digits 1 to 9, at most one time each, to make a true statement.
Hint
What digits would be challenging as denominators?
What digits would be challenging as numerators?
What digits would be challenging as numerators?
Answer
There are many answers. Here are two possibilities:
2/8 + 1/4 = 3/6
1/2 + 3/9 = 5/6
2/8 + 1/4 = 3/6
1/2 + 3/9 = 5/6
Source: Owen Kaplinsky
Another two answers discovered by my students: 1/2 + 9/6 = 8/4 and 5/3 + 2/6 = 8/4
2/4 + 1/3 = 12/10 simply it and get 5/6
6/8 + 1/2 = 5/4
9/3 + 4/2 = 5/1
2/1 + 6/9 = 8/3
7/2 + 3/6 = 4/1
8/2 + 9/3 = 7/1
8/4 + 6/2 = 5/1
8/4 + 9/3 = 5/1
4/2 + 6/2 = 5/1
2/8 + 6/3 = 9/4
54 unique solutions (times 2, if you count it as a different solution if you swap the two addends):
1/4 + 2/8 = 3/6 = 0.5
1/6 + 3/9 = 2/4 = 0.5
1/6 + 3/9 = 4/8 = 0.5
1/6 + 4/8 = 2/3 = 0.6667
1/2 + 3/9 = 5/6 = 0.8333
1/3 + 2/4 = 5/6 = 0.8333
1/3 + 4/8 = 5/6 = 0.8333
2/4 + 3/9 = 5/6 = 0.8333
3/9 + 4/8 = 5/6 = 0.8333
2/3 + 4/8 = 7/6 = 1.1667
1/2 + 6/8 = 5/4 = 1.25
1/2 + 5/6 = 4/3 = 1.3333
2/8 + 5/4 = 9/6 = 1.5
1/2 + 7/6 = 5/3 = 1.6667
2/4 + 7/6 = 5/3 = 1.6667
4/8 + 7/6 = 5/3 = 1.6667
2/8 + 9/6 = 7/4 = 1.75
1/2 + 9/6 = 8/4 = 2.0
2/6 + 5/3 = 8/4 = 2.0
2/8 + 7/4 = 6/3 = 2.0
4/3 + 6/9 = 2/1 = 2.0
4/8 + 9/6 = 2/1 = 2.0
5/4 + 6/8 = 2/1 = 2.0
2/8 + 6/3 = 9/4 = 2.25
3/2 + 6/8 = 9/4 = 2.25
2/6 + 8/4 = 7/3 = 2.3333
1/6 + 7/3 = 5/2 = 2.5
3/6 + 8/4 = 5/2 = 2.5
4/3 + 7/6 = 5/2 = 2.5
4/8 + 6/3 = 5/2 = 2.5
6/8 + 7/4 = 5/2 = 2.5
1/6 + 5/2 = 8/3 = 2.6667
2/1 + 4/6 = 8/3 = 2.6667
2/1 + 6/9 = 8/3 = 2.6667
4/2 + 6/9 = 8/3 = 2.6667
4/8 + 5/2 = 3/1 = 3.0
4/8 + 5/2 = 9/3 = 3.0
6/8 + 9/4 = 3/1 = 3.0
3/1 + 4/8 = 7/2 = 3.5
4/8 + 9/3 = 7/2 = 3.5
5/6 + 8/3 = 7/2 = 3.5
8/4 + 9/6 = 7/2 = 3.5
3/6 + 7/2 = 4/1 = 4.0
5/2 + 9/6 = 4/1 = 4.0
3/1 + 6/4 = 9/2 = 4.5
3/6 + 4/1 = 9/2 = 4.5
3/6 + 9/2 = 5/1 = 5.0
4/2 + 9/3 = 5/1 = 5.0
4/8 + 9/2 = 5/1 = 5.0
6/2 + 8/4 = 5/1 = 5.0
6/4 + 7/2 = 5/1 = 5.0
7/2 + 9/6 = 5/1 = 5.0
8/4 + 9/3 = 5/1 = 5.0
8/2 + 9/3 = 7/1 = 7.0