Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the equation true.
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.