Page:The Rhind Mathematical Papyrus, Volume I.pdf/91

33] Applying $2/3$,$1/undefined$, and $1/undefined$ to 42 we have The total is 40; there remains 2, or $2/3$ of 42. As 1 $1/undefined$$1/undefined$$1/undefined$ applied to 42 gives 97, we shall have as a continuation of our first multiplication

This $1/undefined$ with the product already obtained will make the total 37. Thus the required quantity is 16 $1/undefined$$1/undefined$$2/3$.

Proof.

The whole numbers and larger fractions make 36$1/undefined$$1/undefined$$2/3$ the remainder is $1/undefined$$1/undefined$. The smaller fractions applied to 5432 make

$1/undefined$, $1/undefined$, $1/undefined$, and the fractions of the remainder, $1/undefined$ and $1/undefined$, applied to 5432 make 3621$1/undefined$, 1358, 194, and 194 and 64$1/undefined$; for we have There remains 258$1/undefined$ which is equal to 194 plus 64$1/undefined$.