Because unit fractions were used to represent all fractions, while multiplication was based on repeated doubling, it was important for Ancient Egyptians to know how to double the unit fractions. The Rhind Papyrus includes a decomposition of 2/n in terms of unit fractions, for all odd values of n from 5 to 101. Recall that 2/3 was a standard fraction in its own right.

Divisor (n) Unit Fractions making 2/n
 3two thirds
 5  3   15
 7  4   28
 9  6   18
11  6   66
13  8   52  104
15 10   30
17 12   51   68
19 12   76  114
21 14   42
23 12  276
25 15   75
27 18   54
29 24   58  174  232
31 20  124  155
33 22   66
35 30   42
Divisor (n) Unit Fractions making 2/n
37 24 111 296
39 26   78
41 24  246  328
43 42   86  129  301
45 30   90
47 30  141  470
49 28  196
51 34  102
53 30  318  795
55 30  330
57 38  114
59 36  236  531
61 40  244  488  610
63 42  126
65 39  195
67 40  335  536
69 46  138
Divisor (n) Unit Fractions making 2/n
71  40  568  710
73  60  219  292  365
75  50  150
77  44  308
79  60  237  316  790
81  54  162
83  60  332  415  498
85  51  255
87  58  174
89  60  356  534  890
91  70  130
93  62  186
95  60  380  570
97  56  679  776
99  66  198
101 101  202  303  606

In today's mathematics, we know of various algebraic formulae for constructing these decompositions, for example

2/n = 2/(n+1) + 2/n(n+1) 2/pq = 2/p(p+q) + 2/q(p+q)
and many of the Rhind Papyrus decompositions are of these forms. The derivation of others, however, are harder to understand. For example, the decomposition for 2/15 cannot be obtained using either of these formulae. The importance of 2/3 meant, however, that the Ancient Egyptians knew, and used, the fact that two-thirds of a unit fraction 1/n can be written as

(2/3)(1/n) = 1/2n + 1/6n

and setting n = 5 in this formula gives the decomposition in the table. Whether or not this is how the Rhind Papyrus decomposition was actually obtained, we cannot know.

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