Solution to: Fabulous Fraction
There are 97 solutions to this problem, some of which can easily be calculated on the back of an envelope (such as 1/2 + 3548/7096), and others which are less trivial (such as 34/578 + 96/102).
Here, all possible solutions are shown:
1/2 + 3485/6970, 1/2 + 3548/7096,
1/2 + 3845/7690, 1/2 + 4538/9076,
1/2 + 4685/9370,
1/2 + 4835/9670, 1/2 + 4853/9706,
1/2 + 4865/9730, 1/4 + 7365/9820,
1/6 + 7835/9402, 1/7 + 4362/5089,
2/4 + 3079/6158, 2/6 + 3190/4785,
2/7 + 5940/8316, 2/7 + 6810/9534,
2/9 + 5803/7461, 3/6 + 1485/2970,
3/6 + 2079/4158, 3/6 + 2709/5418,
3/6 + 2907/5814, 3/6 + 4851/9702,
3/127 + 496/508, 4/5 + 1278/6390,
4/5 + 1872/9360, 4/356 + 792/801,
5/104 + 693/728, 6/324 + 795/810,
6/534 + 792/801, 7/9 + 1208/5436,
7/9 + 1352/6084, 7/54 + 893/1026,
8/10 + 729/3645, 8/10 + 927/4635,
8/512 + 693/704, 9/12 + 876/3504,
9/351 + 684/702, 10/28 + 369/574,
10/45 + 287/369, 10/45 + 728/936,
10/96 + 473/528, 12/54 + 609/783,
12/60 + 748/935, 12/96 + 357/408,
12/96 + 735/840, 13/26 + 485/970,
13/52 + 678/904, 15/30 + 486/972,
16/32 + 485/970, 17/89 + 504/623,
18/90 + 276/345, 18/90 + 372/465,
19/57 + 308/462, 19/58 + 273/406,
21/96 + 375/480, 24/63 + 507/819,
24/96 + 531/708, 27/54 + 309/618,
27/81 + 306/459, 27/81 + 630/945,
29/58 + 307/614, 29/87 + 310/465,
31/62 + 485/970, 32/48 + 169/507,
32/80 + 417/695, 34/51 + 269/807,
34/578 + 96/102, 35/70 + 148/296,
35/70 + 481/962, 36/81 + 405/729,
36/81 + 540/972, 38/61 + 207/549,
38/76 + 145/290, 38/76 + 451/902,
38/95 + 426/710, 39/51 + 204/867,
39/65 + 284/710, 42/87 + 315/609,
45/61 + 208/793, 45/90 + 138/276,
45/90 + 186/372, 45/90 + 381/762,
46/92 + 185/370, 48/96 + 135/270,
48/96 + 351/702, 54/87 + 231/609,
56/84 + 109/327, 56/84 + 307/921,
56/428 + 93/107, 56/832 + 97/104,
57/92 + 140/368, 57/204 + 98/136,
59/236 + 78/104, 60/1245 + 79/83,
63/728 + 95/104, 70/96 + 143/528,
74/89 + 105/623, 87/435 + 96/120.
Back to the puzzle