# Using 1/2 as a Benchmark

Directions: Using the digits 1 through 9 only one time each, fill in the blanks to make true statements. For the fraction less than 1/2, try to make the greatest number possible. For the fraction greater than 1/2, try to make the least number possible.

### Hint

How can you use the digits you have remaining to create a fraction that equals 1/2?

Number of Unique Solutions: 394
1: 1/3 < 1/2 and 4/6 > 1/2 and 29/58 = 1/2
2: 1/3 < 1/2 and 4/7 > 1/2 and 28/56 = 1/2
3: 1/3 < 1/2 and 4/7 > 1/2 and 29/58 = 1/2
4: 1/3 < 1/2 and 5/2 > 1/2 and 48/96 = 1/2
5: 1/3 < 1/2 and 5/7 > 1/2 and 46/92 = 1/2
6: 1/3 < 1/2 and 5/7 > 1/2 and 48/96 = 1/2
7: 1/3 < 1/2 and 5/8 > 1/2 and 46/92 = 1/2
8: 1/3 < 1/2 and 6/4 > 1/2 and 29/58 = 1/2
9: 1/3 < 1/2 and 6/7 > 1/2 and 29/58 = 1/2
10: 1/3 < 1/2 and 6/8 > 1/2 and 27/54 = 1/2
11: 1/3 < 1/2 and 6/9 > 1/2 and 27/54 = 1/2
12: 1/3 < 1/2 and 7/2 > 1/2 and 48/96 = 1/2
13: 1/3 < 1/2 and 7/4 > 1/2 and 28/56 = 1/2
14: 1/3 < 1/2 and 7/4 > 1/2 and 29/58 = 1/2
15: 1/3 < 1/2 and 7/5 > 1/2 and 46/92 = 1/2
16: 1/3 < 1/2 and 7/5 > 1/2 and 48/96 = 1/2
17: 1/3 < 1/2 and 7/6 > 1/2 and 29/58 = 1/2
18: 1/3 < 1/2 and 7/8 > 1/2 and 46/92 = 1/2
19: 1/3 < 1/2 and 7/9 > 1/2 and 28/56 = 1/2
20: 1/3 < 1/2 and 8/5 > 1/2 and 46/92 = 1/2
21: 1/3 < 1/2 and 8/6 > 1/2 and 27/54 = 1/2
22: 1/3 < 1/2 and 8/7 > 1/2 and 46/92 = 1/2
23: 1/3 < 1/2 and 8/9 > 1/2 and 27/54 = 1/2
24: 1/3 < 1/2 and 9/4 > 1/2 and 28/56 = 1/2
25: 1/3 < 1/2 and 9/6 > 1/2 and 27/54 = 1/2
26: 1/3 < 1/2 and 9/7 > 1/2 and 28/56 = 1/2
27: 1/3 < 1/2 and 9/8 > 1/2 and 27/54 = 1/2
28: 1/4 < 1/2 and 5/2 > 1/2 and 38/76 = 1/2
29: 1/4 < 1/2 and 5/2 > 1/2 and 39/78 = 1/2
30: 1/4 < 1/2 and 5/6 > 1/2 and 39/78 = 1/2
31: 1/4 < 1/2 and 5/8 > 1/2 and 36/72 = 1/2
32: 1/4 < 1/2 and 5/9 > 1/2 and 36/72 = 1/2
33: 1/4 < 1/2 and 5/9 > 1/2 and 38/76 = 1/2
34: 1/4 < 1/2 and 6/2 > 1/2 and 39/78 = 1/2
35: 1/4 < 1/2 and 6/3 > 1/2 and 29/58 = 1/2
36: 1/4 < 1/2 and 6/5 > 1/2 and 39/78 = 1/2
37: 1/4 < 1/2 and 6/7 > 1/2 and 29/58 = 1/2
38: 1/4 < 1/2 and 7/3 > 1/2 and 28/56 = 1/2
39: 1/4 < 1/2 and 7/3 > 1/2 and 29/58 = 1/2
40: 1/4 < 1/2 and 7/6 > 1/2 and 29/58 = 1/2
41: 1/4 < 1/2 and 7/9 > 1/2 and 28/56 = 1/2
42: 1/4 < 1/2 and 8/5 > 1/2 and 36/72 = 1/2
43: 1/4 < 1/2 and 8/9 > 1/2 and 36/72 = 1/2
44: 1/4 < 1/2 and 9/2 > 1/2 and 38/76 = 1/2
45: 1/4 < 1/2 and 9/3 > 1/2 and 28/56 = 1/2
46: 1/4 < 1/2 and 9/5 > 1/2 and 36/72 = 1/2
47: 1/4 < 1/2 and 9/5 > 1/2 and 38/76 = 1/2
48: 1/4 < 1/2 and 9/7 > 1/2 and 28/56 = 1/2
49: 1/4 < 1/2 and 9/8 > 1/2 and 36/72 = 1/2
50: 1/5 < 1/2 and 2/3 > 1/2 and 48/96 = 1/2
51: 1/5 < 1/2 and 3/2 > 1/2 and 48/96 = 1/2
52: 1/5 < 1/2 and 4/2 > 1/2 and 38/76 = 1/2
53: 1/5 < 1/2 and 4/2 > 1/2 and 39/78 = 1/2
54: 1/5 < 1/2 and 4/6 > 1/2 and 39/78 = 1/2
55: 1/5 < 1/2 and 6/2 > 1/2 and 39/78 = 1/2
56: 1/5 < 1/2 and 6/4 > 1/2 and 39/78 = 1/2
57: 1/5 < 1/2 and 7/2 > 1/2 and 34/68 = 1/2
58: 1/5 < 1/2 and 7/2 > 1/2 and 43/86 = 1/2
59: 1/5 < 1/2 and 7/2 > 1/2 and 48/96 = 1/2
60: 1/5 < 1/2 and 7/3 > 1/2 and 46/92 = 1/2
61: 1/5 < 1/2 and 7/3 > 1/2 and 48/96 = 1/2
62: 1/5 < 1/2 and 7/8 > 1/2 and 23/46 = 1/2
63: 1/5 < 1/2 and 7/8 > 1/2 and 32/64 = 1/2
64: 1/5 < 1/2 and 7/8 > 1/2 and 46/92 = 1/2
65: 1/5 < 1/2 and 7/9 > 1/2 and 23/46 = 1/2
66: 1/5 < 1/2 and 7/9 > 1/2 and 32/64 = 1/2
67: 1/5 < 1/2 and 7/9 > 1/2 and 34/68 = 1/2
68: 1/5 < 1/2 and 7/9 > 1/2 and 43/86 = 1/2
69: 1/5 < 1/2 and 8/3 > 1/2 and 46/92 = 1/2
70: 1/5 < 1/2 and 8/4 > 1/2 and 36/72 = 1/2
71: 1/5 < 1/2 and 8/7 > 1/2 and 23/46 = 1/2
72: 1/5 < 1/2 and 8/7 > 1/2 and 32/64 = 1/2
73: 1/5 < 1/2 and 8/7 > 1/2 and 46/92 = 1/2
74: 1/5 < 1/2 and 8/9 > 1/2 and 23/46 = 1/2
75: 1/5 < 1/2 and 8/9 > 1/2 and 32/64 = 1/2
76: 1/5 < 1/2 and 8/9 > 1/2 and 36/72 = 1/2
77: 1/5 < 1/2 and 9/2 > 1/2 and 34/68 = 1/2
78: 1/5 < 1/2 and 9/2 > 1/2 and 38/76 = 1/2
79: 1/5 < 1/2 and 9/2 > 1/2 and 43/86 = 1/2
80: 1/5 < 1/2 and 9/4 > 1/2 and 36/72 = 1/2
81: 1/5 < 1/2 and 9/4 > 1/2 and 38/76 = 1/2
82: 1/5 < 1/2 and 9/7 > 1/2 and 23/46 = 1/2
83: 1/5 < 1/2 and 9/7 > 1/2 and 32/64 = 1/2
84: 1/5 < 1/2 and 9/7 > 1/2 and 34/68 = 1/2
85: 1/5 < 1/2 and 9/7 > 1/2 and 43/86 = 1/2
86: 1/5 < 1/2 and 9/8 > 1/2 and 23/46 = 1/2
87: 1/5 < 1/2 and 9/8 > 1/2 and 32/64 = 1/2
88: 1/5 < 1/2 and 9/8 > 1/2 and 36/72 = 1/2
89: 1/6 < 1/2 and 3/4 > 1/2 and 29/58 = 1/2
90: 1/6 < 1/2 and 4/2 > 1/2 and 39/78 = 1/2
91: 1/6 < 1/2 and 4/3 > 1/2 and 29/58 = 1/2
92: 1/6 < 1/2 and 4/5 > 1/2 and 39/78 = 1/2
93: 1/6 < 1/2 and 4/7 > 1/2 and 29/58 = 1/2
94: 1/6 < 1/2 and 5/2 > 1/2 and 39/78 = 1/2
95: 1/6 < 1/2 and 5/4 > 1/2 and 39/78 = 1/2
96: 1/6 < 1/2 and 7/3 > 1/2 and 29/58 = 1/2
97: 1/6 < 1/2 and 7/4 > 1/2 and 29/58 = 1/2
98: 1/6 < 1/2 and 8/3 > 1/2 and 27/54 = 1/2
99: 1/6 < 1/2 and 8/9 > 1/2 and 27/54 = 1/2
100: 1/6 < 1/2 and 9/3 > 1/2 and 27/54 = 1/2
101: 1/6 < 1/2 and 9/8 > 1/2 and 27/54 = 1/2
102: 1/7 < 1/2 and 2/3 > 1/2 and 48/96 = 1/2
103: 1/7 < 1/2 and 3/2 > 1/2 and 48/96 = 1/2
104: 1/7 < 1/2 and 3/4 > 1/2 and 28/56 = 1/2
105: 1/7 < 1/2 and 3/4 > 1/2 and 29/58 = 1/2
106: 1/7 < 1/2 and 3/5 > 1/2 and 46/92 = 1/2
107: 1/7 < 1/2 and 3/5 > 1/2 and 48/96 = 1/2
108: 1/7 < 1/2 and 4/3 > 1/2 and 28/56 = 1/2
109: 1/7 < 1/2 and 4/3 > 1/2 and 29/58 = 1/2
110: 1/7 < 1/2 and 4/6 > 1/2 and 29/58 = 1/2
111: 1/7 < 1/2 and 5/2 > 1/2 and 34/68 = 1/2
112: 1/7 < 1/2 and 5/2 > 1/2 and 43/86 = 1/2
113: 1/7 < 1/2 and 5/2 > 1/2 and 48/96 = 1/2
114: 1/7 < 1/2 and 5/3 > 1/2 and 46/92 = 1/2
115: 1/7 < 1/2 and 5/3 > 1/2 and 48/96 = 1/2
116: 1/7 < 1/2 and 5/8 > 1/2 and 23/46 = 1/2
117: 1/7 < 1/2 and 5/8 > 1/2 and 32/64 = 1/2
118: 1/7 < 1/2 and 5/8 > 1/2 and 46/92 = 1/2
119: 1/7 < 1/2 and 5/9 > 1/2 and 23/46 = 1/2
120: 1/7 < 1/2 and 5/9 > 1/2 and 32/64 = 1/2
121: 1/7 < 1/2 and 5/9 > 1/2 and 34/68 = 1/2
122: 1/7 < 1/2 and 5/9 > 1/2 and 43/86 = 1/2
123: 1/7 < 1/2 and 6/3 > 1/2 and 29/58 = 1/2
124: 1/7 < 1/2 and 6/4 > 1/2 and 29/58 = 1/2
125: 1/7 < 1/2 and 8/3 > 1/2 and 46/92 = 1/2
126: 1/7 < 1/2 and 8/5 > 1/2 and 23/46 = 1/2
127: 1/7 < 1/2 and 8/5 > 1/2 and 32/64 = 1/2
128: 1/7 < 1/2 and 8/5 > 1/2 and 46/92 = 1/2
129: 1/7 < 1/2 and 8/9 > 1/2 and 23/46 = 1/2
130: 1/7 < 1/2 and 8/9 > 1/2 and 32/64 = 1/2
131: 1/7 < 1/2 and 9/2 > 1/2 and 34/68 = 1/2
132: 1/7 < 1/2 and 9/2 > 1/2 and 43/86 = 1/2
133: 1/7 < 1/2 and 9/3 > 1/2 and 28/56 = 1/2
134: 1/7 < 1/2 and 9/4 > 1/2 and 28/56 = 1/2
135: 1/7 < 1/2 and 9/5 > 1/2 and 23/46 = 1/2
136: 1/7 < 1/2 and 9/5 > 1/2 and 32/64 = 1/2
137: 1/7 < 1/2 and 9/5 > 1/2 and 34/68 = 1/2
138: 1/7 < 1/2 and 9/5 > 1/2 and 43/86 = 1/2
139: 1/7 < 1/2 and 9/8 > 1/2 and 23/46 = 1/2
140: 1/7 < 1/2 and 9/8 > 1/2 and 32/64 = 1/2
141: 1/8 < 1/2 and 3/5 > 1/2 and 46/92 = 1/2
142: 1/8 < 1/2 and 4/5 > 1/2 and 36/72 = 1/2
143: 1/8 < 1/2 and 5/3 > 1/2 and 46/92 = 1/2
144: 1/8 < 1/2 and 5/4 > 1/2 and 36/72 = 1/2
145: 1/8 < 1/2 and 5/7 > 1/2 and 23/46 = 1/2
146: 1/8 < 1/2 and 5/7 > 1/2 and 32/64 = 1/2
147: 1/8 < 1/2 and 5/7 > 1/2 and 46/92 = 1/2
148: 1/8 < 1/2 and 5/9 > 1/2 and 23/46 = 1/2
149: 1/8 < 1/2 and 5/9 > 1/2 and 32/64 = 1/2
150: 1/8 < 1/2 and 5/9 > 1/2 and 36/72 = 1/2
151: 1/8 < 1/2 and 6/3 > 1/2 and 27/54 = 1/2
152: 1/8 < 1/2 and 6/9 > 1/2 and 27/54 = 1/2
153: 1/8 < 1/2 and 7/3 > 1/2 and 46/92 = 1/2
154: 1/8 < 1/2 and 7/5 > 1/2 and 23/46 = 1/2
155: 1/8 < 1/2 and 7/5 > 1/2 and 32/64 = 1/2
156: 1/8 < 1/2 and 7/5 > 1/2 and 46/92 = 1/2
157: 1/8 < 1/2 and 7/9 > 1/2 and 23/46 = 1/2
158: 1/8 < 1/2 and 7/9 > 1/2 and 32/64 = 1/2
159: 1/8 < 1/2 and 9/3 > 1/2 and 27/54 = 1/2
160: 1/8 < 1/2 and 9/4 > 1/2 and 36/72 = 1/2
161: 1/8 < 1/2 and 9/5 > 1/2 and 23/46 = 1/2
162: 1/8 < 1/2 and 9/5 > 1/2 and 32/64 = 1/2
163: 1/8 < 1/2 and 9/5 > 1/2 and 36/72 = 1/2
164: 1/8 < 1/2 and 9/6 > 1/2 and 27/54 = 1/2
165: 1/8 < 1/2 and 9/7 > 1/2 and 23/46 = 1/2
166: 1/8 < 1/2 and 9/7 > 1/2 and 32/64 = 1/2
167: 1/9 < 1/2 and 3/4 > 1/2 and 28/56 = 1/2
168: 1/9 < 1/2 and 4/2 > 1/2 and 38/76 = 1/2
169: 1/9 < 1/2 and 4/3 > 1/2 and 28/56 = 1/2
170: 1/9 < 1/2 and 4/5 > 1/2 and 36/72 = 1/2
171: 1/9 < 1/2 and 4/5 > 1/2 and 38/76 = 1/2
172: 1/9 < 1/2 and 4/7 > 1/2 and 28/56 = 1/2
173: 1/9 < 1/2 and 5/2 > 1/2 and 34/68 = 1/2
174: 1/9 < 1/2 and 5/2 > 1/2 and 38/76 = 1/2
175: 1/9 < 1/2 and 5/2 > 1/2 and 43/86 = 1/2
176: 1/9 < 1/2 and 5/4 > 1/2 and 36/72 = 1/2
177: 1/9 < 1/2 and 5/4 > 1/2 and 38/76 = 1/2
178: 1/9 < 1/2 and 5/7 > 1/2 and 23/46 = 1/2
179: 1/9 < 1/2 and 5/7 > 1/2 and 32/64 = 1/2
180: 1/9 < 1/2 and 5/7 > 1/2 and 34/68 = 1/2
181: 1/9 < 1/2 and 5/7 > 1/2 and 43/86 = 1/2
182: 1/9 < 1/2 and 5/8 > 1/2 and 23/46 = 1/2
183: 1/9 < 1/2 and 5/8 > 1/2 and 32/64 = 1/2
184: 1/9 < 1/2 and 5/8 > 1/2 and 36/72 = 1/2
185: 1/9 < 1/2 and 6/3 > 1/2 and 27/54 = 1/2
186: 1/9 < 1/2 and 6/8 > 1/2 and 27/54 = 1/2
187: 1/9 < 1/2 and 7/2 > 1/2 and 34/68 = 1/2
188: 1/9 < 1/2 and 7/2 > 1/2 and 43/86 = 1/2
189: 1/9 < 1/2 and 7/3 > 1/2 and 28/56 = 1/2
190: 1/9 < 1/2 and 7/4 > 1/2 and 28/56 = 1/2
191: 1/9 < 1/2 and 7/5 > 1/2 and 23/46 = 1/2
192: 1/9 < 1/2 and 7/5 > 1/2 and 32/64 = 1/2
193: 1/9 < 1/2 and 7/5 > 1/2 and 34/68 = 1/2
194: 1/9 < 1/2 and 7/5 > 1/2 and 43/86 = 1/2
195: 1/9 < 1/2 and 7/8 > 1/2 and 23/46 = 1/2
196: 1/9 < 1/2 and 7/8 > 1/2 and 32/64 = 1/2
197: 1/9 < 1/2 and 8/3 > 1/2 and 27/54 = 1/2
198: 1/9 < 1/2 and 8/4 > 1/2 and 36/72 = 1/2
199: 1/9 < 1/2 and 8/5 > 1/2 and 23/46 = 1/2
200: 1/9 < 1/2 and 8/5 > 1/2 and 32/64 = 1/2
201: 1/9 < 1/2 and 8/5 > 1/2 and 36/72 = 1/2
202: 1/9 < 1/2 and 8/6 > 1/2 and 27/54 = 1/2
203: 1/9 < 1/2 and 8/7 > 1/2 and 23/46 = 1/2
204: 1/9 < 1/2 and 8/7 > 1/2 and 32/64 = 1/2
205: 2/5 < 1/2 and 3/1 > 1/2 and 48/96 = 1/2
206: 2/5 < 1/2 and 4/1 > 1/2 and 38/76 = 1/2
207: 2/5 < 1/2 and 4/1 > 1/2 and 39/78 = 1/2
208: 2/5 < 1/2 and 4/6 > 1/2 and 19/38 = 1/2
209: 2/5 < 1/2 and 4/6 > 1/2 and 39/78 = 1/2
210: 2/5 < 1/2 and 4/7 > 1/2 and 18/36 = 1/2
211: 2/5 < 1/2 and 4/7 > 1/2 and 19/38 = 1/2
212: 2/5 < 1/2 and 6/1 > 1/2 and 39/78 = 1/2
213: 2/5 < 1/2 and 6/4 > 1/2 and 19/38 = 1/2
214: 2/5 < 1/2 and 6/4 > 1/2 and 39/78 = 1/2
215: 2/5 < 1/2 and 6/7 > 1/2 and 19/38 = 1/2
216: 2/5 < 1/2 and 6/8 > 1/2 and 17/34 = 1/2
217: 2/5 < 1/2 and 6/9 > 1/2 and 17/34 = 1/2
218: 2/5 < 1/2 and 7/1 > 1/2 and 34/68 = 1/2
219: 2/5 < 1/2 and 7/1 > 1/2 and 43/86 = 1/2
220: 2/5 < 1/2 and 7/1 > 1/2 and 48/96 = 1/2
221: 2/5 < 1/2 and 7/3 > 1/2 and 48/96 = 1/2
222: 2/5 < 1/2 and 7/4 > 1/2 and 18/36 = 1/2
223: 2/5 < 1/2 and 7/4 > 1/2 and 19/38 = 1/2
224: 2/5 < 1/2 and 7/6 > 1/2 and 19/38 = 1/2
225: 2/5 < 1/2 and 7/9 > 1/2 and 18/36 = 1/2
226: 2/5 < 1/2 and 7/9 > 1/2 and 34/68 = 1/2
227: 2/5 < 1/2 and 7/9 > 1/2 and 43/86 = 1/2
228: 2/5 < 1/2 and 8/6 > 1/2 and 17/34 = 1/2
229: 2/5 < 1/2 and 8/9 > 1/2 and 17/34 = 1/2
230: 2/5 < 1/2 and 9/1 > 1/2 and 34/68 = 1/2
231: 2/5 < 1/2 and 9/1 > 1/2 and 38/76 = 1/2
232: 2/5 < 1/2 and 9/1 > 1/2 and 43/86 = 1/2
233: 2/5 < 1/2 and 9/4 > 1/2 and 18/36 = 1/2
234: 2/5 < 1/2 and 9/4 > 1/2 and 38/76 = 1/2
235: 2/5 < 1/2 and 9/6 > 1/2 and 17/34 = 1/2
236: 2/5 < 1/2 and 9/7 > 1/2 and 18/36 = 1/2
237: 2/5 < 1/2 and 9/7 > 1/2 and 34/68 = 1/2
238: 2/5 < 1/2 and 9/7 > 1/2 and 43/86 = 1/2
239: 2/5 < 1/2 and 9/8 > 1/2 and 17/34 = 1/2
240: 2/6 < 1/2 and 4/1 > 1/2 and 39/78 = 1/2
241: 2/6 < 1/2 and 4/5 > 1/2 and 19/38 = 1/2
242: 2/6 < 1/2 and 4/5 > 1/2 and 39/78 = 1/2
243: 2/6 < 1/2 and 4/7 > 1/2 and 19/38 = 1/2
244: 2/6 < 1/2 and 5/1 > 1/2 and 39/78 = 1/2
245: 2/6 < 1/2 and 5/4 > 1/2 and 19/38 = 1/2
246: 2/6 < 1/2 and 5/4 > 1/2 and 39/78 = 1/2
247: 2/6 < 1/2 and 5/7 > 1/2 and 19/38 = 1/2
248: 2/6 < 1/2 and 5/8 > 1/2 and 17/34 = 1/2
249: 2/6 < 1/2 and 5/9 > 1/2 and 17/34 = 1/2
250: 2/6 < 1/2 and 7/4 > 1/2 and 19/38 = 1/2
251: 2/6 < 1/2 and 7/5 > 1/2 and 19/38 = 1/2
252: 2/6 < 1/2 and 8/5 > 1/2 and 17/34 = 1/2
253: 2/6 < 1/2 and 8/9 > 1/2 and 17/34 = 1/2
254: 2/6 < 1/2 and 9/5 > 1/2 and 17/34 = 1/2
255: 2/6 < 1/2 and 9/8 > 1/2 and 17/34 = 1/2
256: 2/7 < 1/2 and 3/1 > 1/2 and 48/96 = 1/2
257: 2/7 < 1/2 and 3/5 > 1/2 and 48/96 = 1/2
258: 2/7 < 1/2 and 4/5 > 1/2 and 18/36 = 1/2
259: 2/7 < 1/2 and 4/5 > 1/2 and 19/38 = 1/2
260: 2/7 < 1/2 and 4/6 > 1/2 and 19/38 = 1/2
261: 2/7 < 1/2 and 5/1 > 1/2 and 34/68 = 1/2
262: 2/7 < 1/2 and 5/1 > 1/2 and 43/86 = 1/2
263: 2/7 < 1/2 and 5/1 > 1/2 and 48/96 = 1/2
264: 2/7 < 1/2 and 5/3 > 1/2 and 48/96 = 1/2
265: 2/7 < 1/2 and 5/4 > 1/2 and 18/36 = 1/2
266: 2/7 < 1/2 and 5/4 > 1/2 and 19/38 = 1/2
267: 2/7 < 1/2 and 5/6 > 1/2 and 19/38 = 1/2
268: 2/7 < 1/2 and 5/9 > 1/2 and 18/36 = 1/2
269: 2/7 < 1/2 and 5/9 > 1/2 and 34/68 = 1/2
270: 2/7 < 1/2 and 5/9 > 1/2 and 43/86 = 1/2
271: 2/7 < 1/2 and 6/4 > 1/2 and 19/38 = 1/2
272: 2/7 < 1/2 and 6/5 > 1/2 and 19/38 = 1/2
273: 2/7 < 1/2 and 9/1 > 1/2 and 34/68 = 1/2
274: 2/7 < 1/2 and 9/1 > 1/2 and 43/86 = 1/2
275: 2/7 < 1/2 and 9/4 > 1/2 and 18/36 = 1/2
276: 2/7 < 1/2 and 9/5 > 1/2 and 18/36 = 1/2
277: 2/7 < 1/2 and 9/5 > 1/2 and 34/68 = 1/2
278: 2/7 < 1/2 and 9/5 > 1/2 and 43/86 = 1/2
279: 2/8 < 1/2 and 5/6 > 1/2 and 17/34 = 1/2
280: 2/8 < 1/2 and 5/9 > 1/2 and 17/34 = 1/2
281: 2/8 < 1/2 and 6/5 > 1/2 and 17/34 = 1/2
282: 2/8 < 1/2 and 6/9 > 1/2 and 17/34 = 1/2
283: 2/8 < 1/2 and 9/5 > 1/2 and 17/34 = 1/2
284: 2/8 < 1/2 and 9/6 > 1/2 and 17/34 = 1/2
285: 2/9 < 1/2 and 4/1 > 1/2 and 38/76 = 1/2
286: 2/9 < 1/2 and 4/5 > 1/2 and 18/36 = 1/2
287: 2/9 < 1/2 and 4/5 > 1/2 and 38/76 = 1/2
288: 2/9 < 1/2 and 4/7 > 1/2 and 18/36 = 1/2
289: 2/9 < 1/2 and 5/1 > 1/2 and 34/68 = 1/2
290: 2/9 < 1/2 and 5/1 > 1/2 and 38/76 = 1/2
291: 2/9 < 1/2 and 5/1 > 1/2 and 43/86 = 1/2
292: 2/9 < 1/2 and 5/4 > 1/2 and 18/36 = 1/2
293: 2/9 < 1/2 and 5/4 > 1/2 and 38/76 = 1/2
294: 2/9 < 1/2 and 5/6 > 1/2 and 17/34 = 1/2
295: 2/9 < 1/2 and 5/7 > 1/2 and 18/36 = 1/2
296: 2/9 < 1/2 and 5/7 > 1/2 and 34/68 = 1/2
297: 2/9 < 1/2 and 5/7 > 1/2 and 43/86 = 1/2
298: 2/9 < 1/2 and 5/8 > 1/2 and 17/34 = 1/2
299: 2/9 < 1/2 and 6/5 > 1/2 and 17/34 = 1/2
300: 2/9 < 1/2 and 6/8 > 1/2 and 17/34 = 1/2
301: 2/9 < 1/2 and 7/1 > 1/2 and 34/68 = 1/2
302: 2/9 < 1/2 and 7/1 > 1/2 and 43/86 = 1/2
303: 2/9 < 1/2 and 7/4 > 1/2 and 18/36 = 1/2
304: 2/9 < 1/2 and 7/5 > 1/2 and 18/36 = 1/2
305: 2/9 < 1/2 and 7/5 > 1/2 and 34/68 = 1/2
306: 2/9 < 1/2 and 7/5 > 1/2 and 43/86 = 1/2
307: 2/9 < 1/2 and 8/5 > 1/2 and 17/34 = 1/2
308: 2/9 < 1/2 and 8/6 > 1/2 and 17/34 = 1/2
309: 3/7 < 1/2 and 2/1 > 1/2 and 48/96 = 1/2
310: 3/7 < 1/2 and 4/1 > 1/2 and 28/56 = 1/2
311: 3/7 < 1/2 and 4/1 > 1/2 and 29/58 = 1/2
312: 3/7 < 1/2 and 4/6 > 1/2 and 29/58 = 1/2
313: 3/7 < 1/2 and 5/1 > 1/2 and 46/92 = 1/2
314: 3/7 < 1/2 and 5/1 > 1/2 and 48/96 = 1/2
315: 3/7 < 1/2 and 5/2 > 1/2 and 48/96 = 1/2
316: 3/7 < 1/2 and 5/6 > 1/2 and 14/28 = 1/2
317: 3/7 < 1/2 and 5/6 > 1/2 and 41/82 = 1/2
318: 3/7 < 1/2 and 5/8 > 1/2 and 46/92 = 1/2
319: 3/7 < 1/2 and 5/9 > 1/2 and 14/28 = 1/2
320: 3/7 < 1/2 and 5/9 > 1/2 and 41/82 = 1/2
321: 3/7 < 1/2 and 6/1 > 1/2 and 29/58 = 1/2
322: 3/7 < 1/2 and 6/4 > 1/2 and 29/58 = 1/2
323: 3/7 < 1/2 and 6/5 > 1/2 and 14/28 = 1/2
324: 3/7 < 1/2 and 6/5 > 1/2 and 41/82 = 1/2
325: 3/7 < 1/2 and 6/9 > 1/2 and 14/28 = 1/2
326: 3/7 < 1/2 and 6/9 > 1/2 and 41/82 = 1/2
327: 3/7 < 1/2 and 8/1 > 1/2 and 46/92 = 1/2
328: 3/7 < 1/2 and 8/5 > 1/2 and 46/92 = 1/2
329: 3/7 < 1/2 and 9/1 > 1/2 and 28/56 = 1/2
330: 3/7 < 1/2 and 9/4 > 1/2 and 28/56 = 1/2
331: 3/7 < 1/2 and 9/5 > 1/2 and 14/28 = 1/2
332: 3/7 < 1/2 and 9/5 > 1/2 and 41/82 = 1/2
333: 3/7 < 1/2 and 9/6 > 1/2 and 14/28 = 1/2
334: 3/7 < 1/2 and 9/6 > 1/2 and 41/82 = 1/2
335: 3/8 < 1/2 and 5/1 > 1/2 and 46/92 = 1/2
336: 3/8 < 1/2 and 5/7 > 1/2 and 46/92 = 1/2
337: 3/8 < 1/2 and 6/1 > 1/2 and 27/54 = 1/2
338: 3/8 < 1/2 and 6/9 > 1/2 and 27/54 = 1/2
339: 3/8 < 1/2 and 7/1 > 1/2 and 46/92 = 1/2
340: 3/8 < 1/2 and 7/5 > 1/2 and 46/92 = 1/2
341: 3/8 < 1/2 and 9/1 > 1/2 and 27/54 = 1/2
342: 3/8 < 1/2 and 9/6 > 1/2 and 27/54 = 1/2
343: 3/9 < 1/2 and 4/1 > 1/2 and 28/56 = 1/2
344: 3/9 < 1/2 and 4/7 > 1/2 and 28/56 = 1/2
345: 3/9 < 1/2 and 5/6 > 1/2 and 14/28 = 1/2
346: 3/9 < 1/2 and 5/6 > 1/2 and 41/82 = 1/2
347: 3/9 < 1/2 and 5/7 > 1/2 and 14/28 = 1/2
348: 3/9 < 1/2 and 5/7 > 1/2 and 41/82 = 1/2
349: 3/9 < 1/2 and 6/1 > 1/2 and 27/54 = 1/2
350: 3/9 < 1/2 and 6/5 > 1/2 and 14/28 = 1/2
351: 3/9 < 1/2 and 6/5 > 1/2 and 41/82 = 1/2
352: 3/9 < 1/2 and 6/7 > 1/2 and 14/28 = 1/2
353: 3/9 < 1/2 and 6/7 > 1/2 and 41/82 = 1/2
354: 3/9 < 1/2 and 6/8 > 1/2 and 27/54 = 1/2
355: 3/9 < 1/2 and 7/1 > 1/2 and 28/56 = 1/2
356: 3/9 < 1/2 and 7/4 > 1/2 and 28/56 = 1/2
357: 3/9 < 1/2 and 7/5 > 1/2 and 14/28 = 1/2
358: 3/9 < 1/2 and 7/5 > 1/2 and 41/82 = 1/2
359: 3/9 < 1/2 and 7/6 > 1/2 and 14/28 = 1/2
360: 3/9 < 1/2 and 7/6 > 1/2 and 41/82 = 1/2
361: 3/9 < 1/2 and 8/1 > 1/2 and 27/54 = 1/2
362: 3/9 < 1/2 and 8/6 > 1/2 and 27/54 = 1/2
363: 4/9 < 1/2 and 2/1 > 1/2 and 38/76 = 1/2
364: 4/9 < 1/2 and 3/1 > 1/2 and 28/56 = 1/2
365: 4/9 < 1/2 and 5/1 > 1/2 and 36/72 = 1/2
366: 4/9 < 1/2 and 5/1 > 1/2 and 38/76 = 1/2
367: 4/9 < 1/2 and 5/2 > 1/2 and 18/36 = 1/2
368: 4/9 < 1/2 and 5/2 > 1/2 and 38/76 = 1/2
369: 4/9 < 1/2 and 5/7 > 1/2 and 13/26 = 1/2
370: 4/9 < 1/2 and 5/7 > 1/2 and 16/32 = 1/2
371: 4/9 < 1/2 and 5/7 > 1/2 and 18/36 = 1/2
372: 4/9 < 1/2 and 5/7 > 1/2 and 31/62 = 1/2
373: 4/9 < 1/2 and 5/8 > 1/2 and 13/26 = 1/2
374: 4/9 < 1/2 and 5/8 > 1/2 and 16/32 = 1/2
375: 4/9 < 1/2 and 5/8 > 1/2 and 31/62 = 1/2
376: 4/9 < 1/2 and 5/8 > 1/2 and 36/72 = 1/2
377: 4/9 < 1/2 and 7/1 > 1/2 and 28/56 = 1/2
378: 4/9 < 1/2 and 7/2 > 1/2 and 18/36 = 1/2
379: 4/9 < 1/2 and 7/3 > 1/2 and 28/56 = 1/2
380: 4/9 < 1/2 and 7/5 > 1/2 and 13/26 = 1/2
381: 4/9 < 1/2 and 7/5 > 1/2 and 16/32 = 1/2
382: 4/9 < 1/2 and 7/5 > 1/2 and 18/36 = 1/2
383: 4/9 < 1/2 and 7/5 > 1/2 and 31/62 = 1/2
384: 4/9 < 1/2 and 7/8 > 1/2 and 13/26 = 1/2
385: 4/9 < 1/2 and 7/8 > 1/2 and 16/32 = 1/2
386: 4/9 < 1/2 and 7/8 > 1/2 and 31/62 = 1/2
387: 4/9 < 1/2 and 8/1 > 1/2 and 36/72 = 1/2
388: 4/9 < 1/2 and 8/5 > 1/2 and 13/26 = 1/2
389: 4/9 < 1/2 and 8/5 > 1/2 and 16/32 = 1/2
390: 4/9 < 1/2 and 8/5 > 1/2 and 31/62 = 1/2
391: 4/9 < 1/2 and 8/5 > 1/2 and 36/72 = 1/2
392: 4/9 < 1/2 and 8/7 > 1/2 and 13/26 = 1/2
393: 4/9 < 1/2 and 8/7 > 1/2 and 16/32 = 1/2
394: 4/9 < 1/2 and 8/7 > 1/2 and 31/62 = 1/2

Source: Alyson Eaglen

## Product Close to 1,000

Directions: Using the digits 1 to 9 at most one time each, place a digit …

1. 1/5 1/2 and 22/44= 1/2

2. 1/3 1/2 and 48/96 = 1/2

3. 3/9 1/2 and 14/28 = 1/2

4. 14>12and 47>12and 20 100 >12

5. 1/5 1/2 7/9 1/2 34/68=1/2

6. 1/41/2 and 1/4+1/4=1/2

7. 4/91/2 and 13/26=1/2