Page:The Rhind Mathematical Papyrus, Volume I.pdf/20

4. In most of the multiplications all through the papyrus the author checks those multipliers that he is to use. Division was performed by successive multiplication of the divisor until the dividend was obtained.

For the numbers of the descending series they had:

1. A notation which for reciprocal numbers was nearly like their notation for integers, these numbers being distinguished from integers by having a dot in hieratic and the sign in hieroglyphic written over them, except that the ﬁrst three had special signs in hieratic, and the first, ½, in hieroglyphic also;

2. Special devices for addition and subtraction, because it was necessary to express the result using only integers and different unit fractions (see page 3, footnote 1); and for multiplication, because, apparently the only fractions that they could use as direct multipliers were ⅔. ½, and $1/undefined$.

Addition and subtraction will be explained below. In multiplication they generally took ⅔ and then halved to get ⅓, and they took $1/undefined$