## Wednesday, January 12, 2011

### Patterns with division

1/7 = 0.142857142857142857...

Take 142857, split it and then add the parts

142 + 857 = 999
14 + 28 + 57 = 99

2/7 = 0.285714285714285714....

285714 :

285 + 714 = 999
28 + 57 + 14 = 99

3/7 = 0.428571428571428571...

428571 :

428 + 571 = 999
42 + 85 + 71 = 198 = 2 * 99

4/7 = 0.571428571428571428....

571428

571 + 428 = 999
57 + 14 + 28 = 99

5/7 = 0.714285714285714285...

714285 :

714 + 285 = 999
71 + 42 + 85 = 198 = 2 * 99

6/7 = 0.857142857142857142...

857142 :

857 + 142 = 999
85 + 71 + 42 = 198 = 2 * 99

1/13 = 0.076923076923076923....
076 + 923 = 999
07 + 69 + 23 = 99

2/13 = 0.153846153846153846....
153 + 846 = 999
15 + 38 + 46 = 99

3/13 = 0.230769230769230769....
230 + 769 = 999
23 + 07 + 69 = 99

4/13 = 0.307692307692307692....
307 + 692 = 999
30+ 76 + 92 = 198 = 2 * 99

5/13 = 0.384615384615384615....
384 + 615 = 999
38 + 46 + 15 = 99

6/13 = 0.461538461538461538....
461 + 538 = 999
46 + 15 + 38 = 99

7/13 = 0.538461538461538461....
538 + 461 = 999
53 + 84 + 61 = 198 = 2 * 99

8/13 = 0.615384615384615384....
615 + 384 = 999
61 + 53 + 84 = 198 = 2 * 99

9/13 = 0.692307692307692307....
692 + 307 = 999
69 + 23 + 07 = 99

10/13 = 0.769230769230769230....
769 + 230 = 999
76 + 92 + 30 = 198 = 2 * 99

11/13 = 0.846153846153846153....
846 + 153 = 999
84 + 61 + 53 = 198 = 2 * 99

12/13 = 0.923076923076923076....
923 + 076 = 999
92 + 30 + 76 = 198 = 2 * 99

To Be Continued