Science 16*9 Two-thirds seems to have been a primary concept, and the Egyptian could write down f of a number without calculation. One-third was obtained by halving f, which was regarded as 'the two parts' of a length divided in three parts, J being 'the third (and last) part'. (Cf. Genesis xlvii. 24.) Even now, we say 'three parts full', where division into four parts is tacitly assumed. It should be noted that f is, in fact, equivalent to ^, and that, as for i|, both the Greeks and the Romans had a special word for it. (Cf. German—anderthalb.) With such a cumbrous system of fractional notation, calcula- tion was a lengthy process, frequently involving the use of very small fractions, e.g. 5^5 occurs. There was a danger, too, that a number of fractions might be set down without realizing that they would readily combine to form one or more simpler fractions. The system of unit fractions survived long after the use of mixed fractions had become general. It is found, with the same exceptional treatment of f, in the papyrus of Akhmim, written in Greek about A.D. 600. Modern Stock Exchange quotations in Cairo are still often given in the same form, e.g. 98 £ ^ ^ in excess of J conveys a clearer meaning than }|. It is not difficult to see how the fractional notation originated in practical problems dealing with division of food and other commodities. The word 'division5 originally meant partition in two. Suppose 5 loaves are to be divided among 6 persons— an actual problem. The primitive method, still in use in remote parts of the world to-day, is to divide each loaf in half, and give one half to each person. The remaining 4 half loaves are again divided. Of the 8 portions, I is distributed to each individual, leaving 2 quarter loaves over. Each of these is divided in three, giving one portion to each person, who has thus received i J ^ of a loaf. To the Egyptian, this was a complicated process, because of the limitations of his notation. To us, who can write {, it presents no difficulty.