Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box so that the fraction equals the decimal.
Hint
What are easier decimals to find fraction equivalents for?
Answer
Number of Unique Solutions: 56
1: 17 / 25 = 0.68
2: 17 / 68 = 0.25
3: 18 / 24 = 0.75
4: 18 / 75 = 0.24
5: 19 / 25 = 0.76
6: 19 / 76 = 0.25
7: 36 / 15 = 2.40
8: 36 / 24 = 1.50
9: 36 / 48 = 0.75
10: 36 / 75 = 0.48
11: 37 / 04 = 9.25
12: 37 / 20 = 1.85
13: 37 / 25 = 1.48
14: 39 / 15 = 2.60
15: 39 / 26 = 1.50
16: 48 / 15 = 3.20
17: 48 / 32 = 1.50
18: 49 / 28 = 1.75
19: 60 / 48 = 1.25
20: 63 / 15 = 4.20
21: 63 / 42 = 1.50
22: 63 / 75 = 0.84
23: 63 / 84 = 0.75
24: 64 / 50 = 1.28
25: 67 / 50 = 1.34
26: 69 / 20 = 3.45
27: 69 / 50 = 1.38
28: 72 / 15 = 4.80
29: 72 / 16 = 4.50
30: 72 / 45 = 1.60
31: 72 / 48 = 1.50
32: 73 / 50 = 1.46
33: 74 / 08 = 9.25
34: 76 / 25 = 3.04
35: 78 / 12 = 6.50
36: 78 / 40 = 1.95
37: 78 / 65 = 1.20
38: 79 / 25 = 3.16
39: 80 / 64 = 1.25
40: 83 / 20 = 4.15
41: 86 / 40 = 2.15
42: 86 / 50 = 1.72
43: 87 / 20 = 4.35
44: 87 / 60 = 1.45
45: 90 / 24 = 3.75
46: 91 / 25 = 3.64
47: 91 / 26 = 3.50
48: 91 / 35 = 2.60
49: 93 / 15 = 6.20
50: 93 / 20 = 4.65
51: 93 / 62 = 1.50
52: 93 / 75 = 1.24
53: 94 / 25 = 3.76
54: 96 / 25 = 3.84
55: 96 / 75 = 1.28
56: 97 / 20 = 4.85
1: 17 / 25 = 0.68
2: 17 / 68 = 0.25
3: 18 / 24 = 0.75
4: 18 / 75 = 0.24
5: 19 / 25 = 0.76
6: 19 / 76 = 0.25
7: 36 / 15 = 2.40
8: 36 / 24 = 1.50
9: 36 / 48 = 0.75
10: 36 / 75 = 0.48
11: 37 / 04 = 9.25
12: 37 / 20 = 1.85
13: 37 / 25 = 1.48
14: 39 / 15 = 2.60
15: 39 / 26 = 1.50
16: 48 / 15 = 3.20
17: 48 / 32 = 1.50
18: 49 / 28 = 1.75
19: 60 / 48 = 1.25
20: 63 / 15 = 4.20
21: 63 / 42 = 1.50
22: 63 / 75 = 0.84
23: 63 / 84 = 0.75
24: 64 / 50 = 1.28
25: 67 / 50 = 1.34
26: 69 / 20 = 3.45
27: 69 / 50 = 1.38
28: 72 / 15 = 4.80
29: 72 / 16 = 4.50
30: 72 / 45 = 1.60
31: 72 / 48 = 1.50
32: 73 / 50 = 1.46
33: 74 / 08 = 9.25
34: 76 / 25 = 3.04
35: 78 / 12 = 6.50
36: 78 / 40 = 1.95
37: 78 / 65 = 1.20
38: 79 / 25 = 3.16
39: 80 / 64 = 1.25
40: 83 / 20 = 4.15
41: 86 / 40 = 2.15
42: 86 / 50 = 1.72
43: 87 / 20 = 4.35
44: 87 / 60 = 1.45
45: 90 / 24 = 3.75
46: 91 / 25 = 3.64
47: 91 / 26 = 3.50
48: 91 / 35 = 2.60
49: 93 / 15 = 6.20
50: 93 / 20 = 4.65
51: 93 / 62 = 1.50
52: 93 / 75 = 1.24
53: 94 / 25 = 3.76
54: 96 / 25 = 3.84
55: 96 / 75 = 1.28
56: 97 / 20 = 4.85
Source: Robert Kaplinsky
Also 36/48 = 0.75
Thank you Sandy for contributing! The solution set has been updated.
Thanks – my students got a couple more: 17/25=0.68 and 19/25=0.76
Thanks! I added those as well.
52/16= 3.25
81/36= 2.25
I think I found another one…72/16 = 4.50
Thanks Daniel. I added it.
Great Job daniel I got 19/25 = 0.76
My class found 4 more unless we are making a mistake!!
18/24= 0.75
73/50= 1.46
48/32= 1.50
80/64= 1.25
96/25= 3.84
Also
39/26 = 1.50
72/48 = 1.50
I really like that this problem has many solutions that can keep kids thinking. Math often has more than one correct answer.
76/25=3.04
Any statement with using the digit 0 on it?
My students also found:
78/40=1.95
74/08=9.25
78/65=1.20
86/50=1.72
Students found 37/04 = 9.25
More unlisted solutions:
63/50
82/50
92/50
93/50
Oops, 63/50 = 1.26 which reuses the 6