Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box make an equivalent ratio.
Hint
How can you tell when two ratios are equivalent?
Answer
There are many possible answers including 4:1 = 20:5.
Source: Robert Kaplinsky
5:2 = 10:4
7:3 = 14:6
6:3 = 18:9
4:3 = 12:9
4:2 = 16:18
5:1 = 20:4
6:1 = 18:3
7:1 = 14:2
8:1 = 16:2
9:1 = 18:2
9:2 = 18:4
5:4 = 10:8
9:3 = 18:6
There are 52 without leading zeros:
3/1 = 24/8
3/1 = 27/9
4/1 = 20/5
4/1 = 28/7
4/1 = 32/8
4/1 = 36/9
4/2 = 10/5
4/2 = 16/8
4/2 = 18/9
4/3 = 12/9
5/1 = 20/4
5/1 = 30/6
5/1 = 40/8
5/2 = 10/4
5/3 = 10/6
5/4 = 10/8
6/1 = 30/5
6/1 = 42/7
6/1 = 54/9
6/3 = 10/5
6/3 = 14/7
6/3 = 18/9
6/4 = 12/8
7/1 = 28/4
7/1 = 42/6
7/1 = 56/8
7/1 = 63/9
7/3 = 14/6
7/3 = 21/9
8/1 = 24/3
8/1 = 32/4
8/1 = 40/5
8/1 = 56/7
8/1 = 72/9
8/2 = 16/4
8/2 = 36/9
8/3 = 24/9
8/4 = 10/5
8/4 = 12/6
8/6 = 12/9
9/1 = 27/3
9/1 = 36/4
9/1 = 54/6
9/1 = 63/7
9/1 = 72/8
9/2 = 18/4
9/2 = 36/8
9/3 = 12/4
9/3 = 18/6
9/3 = 21/7
9/3 = 24/8
9/6 = 12/8
Plus 40 solutions with leading zeros:
1/2 = 03/6
1/2 = 04/8
1/3 = 02/6
1/4 = 02/8
2/1 = 06/3
2/1 = 08/4
2/3 = 04/6
2/3 = 06/9
2/4 = 03/6
2/6 = 01/3
2/6 = 03/9
2/8 = 01/4
3/1 = 06/2
3/2 = 06/4
3/2 = 09/6
3/4 = 06/8
3/6 = 01/2
3/6 = 02/4
3/6 = 04/8
3/9 = 02/6
4/1 = 08/2
4/2 = 06/3
4/3 = 08/6
4/6 = 02/3
4/8 = 01/2
4/8 = 03/6
6/2 = 03/1
6/2 = 09/3
6/3 = 02/1
6/3 = 04/2
6/3 = 08/4
6/4 = 03/2
6/8 = 03/4
6/9 = 02/3
8/2 = 04/1
8/4 = 02/1
8/4 = 06/3
8/6 = 04/3
9/3 = 06/2
9/6 = 03/2
This is not a 6th grade problem if you include decimals