Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.
Hint
What fractions less than one and what fractions greater than one might be helpful to use?
Answer
There are multiple answers. Two include:
8/4 x 2/1 + 9/3 = 7
4/6 x 3/2 + 7 = 8
8/4 x 2/1 + 9/3 = 7
4/6 x 3/2 + 7 = 8
Source: Joseph Nguyen
49 solutions (times 4 if you swap the numerators, the denominators or both of the two fractions being multiplied):
2/9 * 3/4 + 5/6 = 1
3/8 * 4/9 + 5/6 = 1
4/8 * 2/3 + 6/9 = 1
4/8 * 6/9 + 2/3 = 1
1/3 * 6/8 + 7/4 = 2
1/4 * 8/6 + 5/3 = 2
3/8 * 6/9 + 7/4 = 2
4/8 * 6/9 + 5/3 = 2
1/3 * 9/6 + 7/2 = 4
5/6 * 2/1 + 7/3 = 4
6/9 * 2/1 + 8/3 = 4
1/3 * 6/4 + 9/2 = 5
2/3 * 9/6 + 4/1 = 5
3/9 * 6/2 + 4/1 = 5
4/8 * 3/1 + 7/2 = 5
4/8 * 9/3 + 7/2 = 5
7/6 * 2/1 + 8/3 = 5
7/6 * 4/2 + 8/3 = 5
8/6 * 2/1 + 7/3 = 5
8/6 * 4/2 + 7/3 = 5
9/6 * 2/1 + 8/4 = 5
9/6 * 8/4 + 2/1 = 5
3/8 * 4/1 + 9/2 = 6
2/1 * 8/4 + 9/3 = 7
3/6 * 8/2 + 5/1 = 7
4/3 * 9/6 + 5/1 = 7
5/4 * 6/3 + 9/2 = 7
5/6 * 3/1 + 9/2 = 7
5/8 * 4/1 + 9/2 = 7
6/3 * 9/4 + 5/2 = 7
2/3 * 6/4 + 7/1 = 8
2/3 * 9/6 + 7/1 = 8
3/6 * 4/2 + 7/1 = 8
3/9 * 6/2 + 7/1 = 8
4/6 * 9/2 + 5/1 = 8
6/3 * 9/4 + 7/2 = 8
6/4 * 3/1 + 7/2 = 8
6/4 * 7/3 + 9/2 = 8
7/6 * 3/1 + 9/2 = 8
9/6 * 3/1 + 7/2 = 8
2/3 * 6/4 + 8/1 = 9
3/2 * 8/4 + 6/1 = 9
3/6 * 4/2 + 8/1 = 9
3/6 * 8/2 + 7/1 = 9
4/2 * 6/3 + 5/1 = 9
5/3 * 6/2 + 4/1 = 9
6/3 * 8/4 + 5/1 = 9
8/4 * 3/1 + 6/2 = 9
8/4 * 6/2 + 3/1 = 9
We also found 2/3 * 4/6 + 5/9 = 1
There are many solutions.
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