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| 1/x | 1/2 | 1/3 | 2/3 | 1/4 | 3/4 | 1/5 | 2/5 | 3/5 | 4/5 | 1/6 | 5/6 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1/2 | 1/4 | 1/6 | 1/3 | 1/8 | 3/8 | 1/10 | 1/5 | 3/10 | 2/5 | 1/12 | 5/12 | |
| 1/3 | 1/6 | 1/9 | 2/9 | 1/12 | 1/4 | 1/15 | 2/15 | 1/5 | 4/15 | 1/18 | 5/18 | |
| 2/3 | 1/3 | 2/9 | 4/9 | 1/6 | 1/2 | 2/15 | 4/15 | 2/5 | 8/15 | 1/9 | 5/9 | |
| 1/4 | 1/8 | 1/12 | 1/6 | 1/16 | 3/16 | 1/20 | 1/10 | 3/20 | 1/5 | 1/24 | 5/24 | |
| 3/4 | 3/8 | 1/4 | 1/2 | 3/16 | 9/16 | 3/20 | 3/10 | 9/20 | 3/5 | 1/8 | 5/8 | |
| 1/5 | 1/10 | 1/15 | 2/15 | 1/20 | 3/20 | 1/25 | 2/25 | 3/25 | 4/25 | 1/30 | 1/6 | |
| 2/5 | 1/5 | 2/15 | 4/15 | 1/10 | 3/10 | 2/25 | 4/25 | 6/25 | 8/25 | 1/15 | 1/3 | |
| 3/5 | 3/10 | 1/5 | 2/5 | 3/20 | 9/20 | 3/25 | 6/25 | 9/25 | 12/25 | 1/10 | 1/2 | |
| 4/5 | 2/5 | 4/15 | 8/15 | 1/5 | 3/5 | 4/25 | 8/25 | 12/25 | 16/25 | 2/15 | 2/3 | |
| 1/6 | 1/12 | 1/18 | 1/9 | 1/24 | 1/8 | 1/30 | 1/15 | 1/10 | 2/15 | 1/36 | 5/36 | |
| 5/6 | 5/12 | 5/18 | 5/9 | 5/24 | 5/8 | 1/6 | 1/3 | 1/2 | 2/3 | 5/36 | 25/36 | |
| 1/7 | 1/14 | 1/21 | 2/21 | 1/28 | 3/28 | 1/35 | 2/35 | 3/35 | 4/35 | 1/42 | 5/42 | |
| 2/7 | 1/7 | 2/21 | 4/21 | 1/14 | 3/14 | 2/35 | 4/35 | 6/35 | 8/35 | 1/21 | 5/21 | |
| 3/7 | 3/14 | 1/7 | 2/7 | 3/28 | 9/28 | 3/35 | 6/35 | 9/35 | 12/35 | 1/14 | 5/14 | |
| 4/7 | 2/7 | 4/21 | 8/21 | 1/7 | 3/7 | 4/35 | 8/35 | 12/35 | 16/35 | 2/21 | 10/21 | |
| 5/7 | 5/14 | 5/21 | 10/21 | 5/28 | 15/28 | 1/7 | 2/7 | 3/7 | 4/7 | 5/42 | 25/42 | |
| 6/7 | 3/7 | 2/7 | 4/7 | 3/14 | 9/14 | 6/35 | 12/35 | 18/35 | 24/35 | 1/7 | 5/7 | |
| 1/8 | 1/16 | 1/24 | 1/12 | 1/32 | 3/32 | 1/40 | 1/20 | 3/40 | 1/10 | 1/48 | 5/48 | |
| 3/8 | 3/16 | 1/8 | 1/4 | 3/32 | 9/32 | 3/40 | 3/20 | 9/40 | 3/10 | 1/16 | 5/16 | |
| 5/8 | 5/16 | 5/24 | 5/12 | 5/32 | 15/32 | 1/8 | 1/4 | 3/8 | 1/2 | 5/48 | 25/48 | |
| 7/8 | 7/16 | 7/24 | 7/12 | 7/32 | 21/32 | 7/40 | 7/20 | 21/40 | 7/10 | 7/48 | 35/48 | |
| 1/9 | 1/18 | 1/27 | 2/27 | 1/36 | 1/12 | 1/45 | 2/45 | 1/15 | 4/45 | 1/54 | 5/54 | |
| 2/9 | 1/9 | 2/27 | 4/27 | 1/18 | 1/6 | 2/45 | 4/45 | 2/15 | 8/45 | 1/27 | 5/27 | |
| 4/9 | 2/9 | 4/27 | 8/27 | 1/9 | 1/3 | 4/45 | 8/45 | 4/15 | 16/45 | 2/27 | 10/27 | |
| 5/9 | 5/18 | 5/27 | 10/27 | 5/36 | 5/12 | 1/9 | 2/9 | 1/3 | 4/9 | 5/54 | 25/54 | |
| 7/9 | 7/18 | 7/27 | 14/27 | 7/36 | 7/12 | 7/45 | 14/45 | 7/15 | 28/45 | 7/54 | 35/54 | |
| 8/9 | 4/9 | 8/27 | 16/27 | 2/9 | 2/3 | 8/45 | 16/45 | 8/15 | 32/45 | 4/27 | 20/27 | |
| 1/x | 1/2 | 1/3 | 2/3 | 1/4 | 3/4 | 1/5 | 2/5 | 3/5 | 4/5 | 1/6 | 5/6 |
| 1/x | 1/7 | 2/7 | 3/7 | 4/7 | 5/7 | 6/7 | 1/8 | 3/8 | 5/8 | 7/8 | 1/9 | 2/9 | 4/9 | 5/9 | 7/9 | 8/9 | 1/x | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1/2 | 1/14 | 1/7 | 3/14 | 2/7 | 5/14 | 3/7 | 1/16 | 3/16 | 5/16 | 7/16 | 1/18 | 1/9 | 2/9 | 5/18 | 7/18 | 4/9 | 1/2 | ||
| 1/3 | 1/21 | 2/21 | 1/7 | 4/21 | 5/21 | 2/7 | 1/24 | 1/8 | 5/24 | 7/24 | 1/27 | 2/27 | 4/27 | 5/27 | 7/27 | 8/27 | 1/3 | ||
| 2/3 | 2/21 | 4/21 | 2/7 | 8/21 | 10/21 | 4/7 | 1/12 | 1/4 | 5/12 | 7/12 | 2/27 | 4/27 | 8/27 | 10/27 | 14/27 | 16/27 | 2/3 | ||
| 1/4 | 1/28 | 1/14 | 3/28 | 1/7 | 5/28 | 3/14 | 1/32 | 3/32 | 5/32 | 7/32 | 1/36 | 1/18 | 1/9 | 5/36 | 7/36 | 2/9 | 1/4 | ||
| 3/4 | 3/28 | 3/14 | 9/28 | 3/7 | 15/28 | 9/14 | 3/32 | 9/32 | 15/32 | 21/32 | 1/12 | 1/6 | 1/3 | 5/12 | 7/12 | 2/3 | 3/4 | ||
| 1/5 | 1/35 | 2/35 | 3/35 | 4/35 | 1/7 | 6/35 | 1/40 | 3/40 | 1/8 | 7/40 | 1/45 | 2/45 | 4/45 | 1/9 | 7/45 | 8/45 | 1/5 | ||
| 2/5 | 2/35 | 4/35 | 6/35 | 8/35 | 2/7 | 12/35 | 1/20 | 3/20 | 1/4 | 7/20 | 2/45 | 4/45 | 8/45 | 2/9 | 14/45 | 16/45 | 2/5 | ||
| 3/5 | 3/35 | 6/35 | 9/35 | 12/35 | 3/7 | 18/35 | 3/40 | 9/40 | 3/8 | 21/40 | 1/15 | 2/15 | 4/15 | 1/3 | 7/15 | 8/15 | 3/5 | ||
| 4/5 | 4/35 | 8/35 | 12/35 | 16/35 | 4/7 | 24/35 | 1/10 | 3/10 | 1/2 | 7/10 | 4/45 | 8/45 | 16/45 | 4/9 | 28/45 | 32/45 | 4/5 | ||
| 1/6 | 1/42 | 1/21 | 1/14 | 2/21 | 5/42 | 1/7 | 1/48 | 1/16 | 5/48 | 7/48 | 1/54 | 1/27 | 2/27 | 5/54 | 7/54 | 4/27 | 1/6 | ||
| 5/6 | 5/42 | 5/21 | 5/14 | 10/21 | 25/42 | 5/7 | 5/48 | 5/16 | 25/48 | 35/48 | 5/54 | 5/27 | 10/27 | 25/54 | 35/54 | 20/27 | 5/6 | ||
| 1/7 | 1/49 | 2/49 | 3/49 | 4/49 | 5/49 | 6/49 | 1/56 | 3/56 | 5/56 | 1/8 | 1/63 | 2/63 | 4/63 | 5/63 | 1/9 | 8/63 | 1/7 | ||
| 2/7 | 2/49 | 4/49 | 6/49 | 8/49 | 10/49 | 12/49 | 1/28 | 3/28 | 5/28 | 1/4 | 2/63 | 4/63 | 8/63 | 10/63 | 2/9 | 16/63 | 2/7 | ||
| 3/7 | 3/49 | 6/49 | 9/49 | 12/49 | 15/49 | 18/49 | 3/56 | 9/56 | 15/56 | 3/8 | 1/21 | 2/21 | 4/21 | 5/21 | 1/3 | 8/21 | 3/7 | ||
| 4/7 | 4/49 | 8/49 | 12/49 | 16/49 | 20/49 | 24/49 | 1/14 | 3/14 | 5/14 | 1/2 | 4/63 | 8/63 | 16/63 | 20/63 | 4/9 | 32/63 | 4/7 | ||
| 5/7 | 5/49 | 10/49 | 15/49 | 20/49 | 25/49 | 30/49 | 5/56 | 15/56 | 25/56 | 5/8 | 5/63 | 10/63 | 20/63 | 25/63 | 5/9 | 40/63 | 5/7 | ||
| 6/7 | 6/49 | 12/49 | 18/49 | 24/49 | 30/49 | 36/49 | 3/28 | 9/28 | 15/28 | 3/4 | 2/21 | 4/21 | 8/21 | 10/21 | 2/3 | 16/21 | 6/7 | ||
| 1/8 | 1/56 | 1/28 | 3/56 | 1/14 | 5/56 | 3/28 | 1/64 | 3/64 | 5/64 | 7/64 | 1/72 | 1/36 | 1/18 | 5/72 | 7/72 | 1/9 | 1/8 | ||
| 3/8 | 3/56 | 3/28 | 9/56 | 3/14 | 15/56 | 9/28 | 3/64 | 9/64 | 15/64 | 21/64 | 1/24 | 1/12 | 1/6 | 5/24 | 7/24 | 1/3 | 3/8 | ||
| 5/8 | 5/56 | 5/28 | 15/56 | 5/14 | 25/56 | 15/28 | 5/64 | 15/64 | 25/64 | 35/64 | 5/72 | 5/36 | 5/18 | 25/72 | 35/72 | 5/9 | 5/8 | ||
| 7/8 | 1/8 | 1/4 | 3/8 | 1/2 | 5/8 | 3/4 | 7/64 | 21/64 | 35/64 | 49/64 | 7/72 | 7/36 | 7/18 | 35/72 | 49/72 | 7/9 | 7/8 | ||
| 1/9 | 1/63 | 2/63 | 1/21 | 4/63 | 5/63 | 2/21 | 1/72 | 1/24 | 5/72 | 7/72 | 1/81 | 2/81 | 4/81 | 5/81 | 7/81 | 8/81 | 1/9 | ||
| 2/9 | 2/63 | 4/63 | 2/21 | 8/63 | 10/63 | 4/21 | 1/36 | 1/12 | 5/36 | 7/36 | 2/81 | 4/81 | 8/81 | 10/81 | 14/81 | 16/81 | 2/9 | ||
| 4/9 | 4/63 | 8/63 | 4/21 | 16/63 | 20/63 | 8/21 | 1/18 | 1/6 | 5/18 | 7/18 | 4/81 | 8/81 | 16/81 | 20/81 | 28/81 | 32/81 | 4/9 | ||
| 5/9 | 5/63 | 10/63 | 5/21 | 20/63 | 25/63 | 10/21 | 5/72 | 5/24 | 25/72 | 35/72 | 5/81 | 10/81 | 20/81 | 25/81 | 35/81 | 40/81 | 5/9 | ||
| 7/9 | 1/9 | 2/9 | 1/3 | 4/9 | 5/9 | 2/3 | 7/72 | 7/24 | 35/72 | 49/72 | 7/81 | 14/81 | 28/81 | 35/81 | 49/81 | 56/81 | 7/9 | ||
| 8/9 | 8/63 | 16/63 | 8/21 | 32/63 | 40/63 | 16/21 | 1/9 | 1/3 | 5/9 | 7/9 | 8/81 | 16/81 | 32/81 | 40/81 | 56/81 | 64/81 | 8/9 | ||
| 1/x | 1/7 | 2/7 | 3/7 | 4/7 | 5/7 | 6/7 | 1/8 | 3/8 | 5/8 | 7/8 | 1/9 | 2/9 | 4/9 | 5/9 | 7/9 | 8/9 | 1/x |
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