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Adding Mixed Numbers 2

Directions: Use the digits 1-9 each once to make a true statement.

Hint

Hint

What assumptions are we making about the fractions we are able to use? Do fractions have to be in lowest terms?

Answer

Answer

Number of Unique Solutions: 100
1: 1 3/2 + 7 6/8 = 9 5/4
2: 1 3/9 + 4 7/2 = 8 5/6
3: 1 4/2 + 5 7/3 = 9 8/6
4: 1 4/3 + 8 7/6 = 9 5/2
5: 1 4/6 + 7 3/9 = 5 8/2
6: 1 5/2 + 3 8/4 = 7 9/6
7: 1 5/2 + 4 8/3 = 9 7/6
8: 1 5/2 + 7 3/6 = 9 8/4
9: 1 5/2 + 7 4/8 = 9 6/3
10: 1 5/3 + 7 8/6 = 9 4/2
11: 1 5/6 + 4 9/2 = 8 7/3
12: 1 6/3 + 7 2/8 = 9 5/4
13: 1 6/8 + 2 9/3 = 5 7/4
14: 1 7/3 + 5 4/2 = 9 8/6
15: 1 7/6 + 8 4/3 = 9 5/2
16: 1 8/3 + 4 5/2 = 9 7/6
17: 1 8/6 + 7 5/3 = 9 4/2
18: 1 9/3 + 2 6/8 = 5 7/4
19: 1 9/3 + 5 4/8 = 6 7/2
20: 1 9/6 + 5 2/8 = 7 3/4
21: 1 9/6 + 5 3/2 = 7 8/4
22: 2 1/3 + 7 4/8 = 9 5/6
23: 2 1/6 + 5 3/9 = 7 4/8
24: 2 3/1 + 5 6/8 = 9 7/4
25: 2 3/9 + 5 1/6 = 7 4/8
26: 2 4/8 + 9 3/6 = 5 7/1
27: 2 4/8 + 9 3/6 = 7 5/1
28: 2 5/1 + 3 6/8 = 9 7/4
29: 2 6/8 + 3 5/1 = 9 7/4
30: 2 6/8 + 5 9/4 = 3 7/1
31: 2 6/9 + 8 4/3 = 7 5/1
32: 2 7/3 + 5 1/6 = 9 4/8
33: 2 9/4 + 5 6/8 = 7 3/1
34: 3 2/1 + 5 6/8 = 9 7/4
35: 3 2/8 + 5 1/4 = 7 9/6
36: 3 4/8 + 5 9/2 = 6 7/1
37: 3 5/2 + 1 8/4 = 7 9/6
38: 3 6/8 + 5 2/1 = 9 7/4
39: 3 9/2 + 5 4/8 = 6 7/1
40: 3 9/2 + 5 4/8 = 7 6/1
41: 4 2/6 + 7 8/3 = 9 5/1
42: 4 2/6 + 9 5/3 = 7 8/1
43: 4 6/2 + 5 9/3 = 7 8/1
44: 4 6/2 + 5 9/3 = 8 7/1
45: 4 8/3 + 7 2/6 = 5 9/1
46: 4 8/3 + 7 2/6 = 9 5/1
47: 4 9/3 + 5 6/2 = 7 8/1
48: 4 9/3 + 5 6/2 = 8 7/1
49: 5 1/2 + 3 6/8 = 7 9/4
50: 5 2/4 + 9 3/6 = 7 8/1
51: 5 2/4 + 9 3/6 = 8 7/1
52: 5 2/8 + 3 1/4 = 7 9/6
53: 5 3/1 + 2 6/8 = 9 7/4
54: 5 3/6 + 9 2/4 = 7 8/1
55: 5 3/6 + 9 2/4 = 8 7/1
56: 5 4/2 + 1 3/9 = 7 8/6
57: 5 4/6 + 7 1/3 = 9 8/2
58: 5 6/4 + 1 7/2 = 8 9/3
59: 5 6/4 + 8 3/2 = 7 9/1
60: 5 6/4 + 8 3/2 = 9 7/1
61: 5 6/8 + 2 9/4 = 3 7/1
62: 5 6/8 + 3 1/2 = 7 9/4
63: 5 7/2 + 1 6/4 = 8 9/3
64: 5 7/3 + 2 1/6 = 9 4/8
65: 5 9/2 + 3 4/8 = 7 6/1
66: 5 9/3 + 1 4/8 = 6 7/2
67: 5 9/4 + 2 6/8 = 7 3/1
68: 5 9/6 + 1 2/8 = 7 3/4
69: 5 9/6 + 1 3/2 = 7 8/4
70: 6 2/8 + 7 3/4 = 5 9/1
71: 6 4/8 + 1 5/2 = 7 9/3
72: 6 5/2 + 1 4/8 = 7 9/3
73: 7 2/3 + 1 5/6 = 9 4/8
74: 7 2/4 + 1 3/9 = 8 5/6
75: 7 2/8 + 1 5/4 = 9 3/6
76: 7 2/8 + 6 3/4 = 5 9/1
77: 7 2/8 + 6 3/4 = 9 5/1
78: 7 3/2 + 1 6/8 = 9 5/4
79: 7 3/4 + 1 6/8 = 5 9/2
80: 7 3/4 + 6 2/8 = 9 5/1
81: 7 4/6 + 1 3/9 = 5 8/2
82: 7 4/6 + 5 1/3 = 9 8/2
83: 7 5/2 + 1 3/6 = 9 8/4
84: 7 5/2 + 1 4/8 = 9 6/3
85: 7 5/4 + 1 2/8 = 9 3/6
86: 7 5/6 + 1 2/3 = 9 4/8
87: 7 6/3 + 1 2/8 = 9 5/4
88: 7 6/8 + 1 3/4 = 5 9/2
89: 7 8/3 + 4 2/6 = 5 9/1
90: 8 4/3 + 2 6/9 = 5 7/1
91: 8 6/4 + 5 3/2 = 7 9/1
92: 8 6/4 + 5 3/2 = 9 7/1
93: 8 6/9 + 2 4/3 = 5 7/1
94: 8 6/9 + 2 4/3 = 7 5/1
95: 8 7/6 + 1 2/4 = 9 5/3
96: 9 2/6 + 4 5/3 = 7 8/1
97: 9 2/6 + 4 5/3 = 8 7/1
98: 9 4/8 + 2 3/6 = 5 7/1
99: 9 4/8 + 2 3/6 = 7 5/1
100: 9 5/3 + 4 2/6 = 8 7/1

Source: Ellen Metzger

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2 comments

  1. Solution found by fifth grade students: 1-5/4 + 7-2/8 = 9-3/6

  2. Solution found by 5th grade students- 4 1/2 + 5 7/3 = 9 8/6

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