Page:The Rhind Mathematical Papyrus, Volume I.pdf/98

Problem 38
I have gone three times into the hekat-measure, my ¹⁄₇ has been added to me, and I return having filled the hekat-measure. What is it that says this?

Assume 1. Multiplying by the given expression we have

\	1	1
\	2	2
\	1⁄7	1⁄7
	Total	31⁄7

Get 1 by operating on 3¹⁄₇.

	1	31⁄7
	1⁄22	1⁄7

for ¹⁄₇ of 22 is 3¹⁄₇,

	1⁄1⁄41⁄28
	1⁄61⁄66	1⁄21⁄14
	Total	1.

Therefore the answer is ¹⁄₆¹⁄₁₁¹⁄₂₂¹⁄₆₆.

Proof.

	1	1⁄61⁄111⁄221⁄66
	2	1⁄21⁄111⁄331⁄66
	1⁄7	1⁄22

for ¹⁄₂₂ of 7 is the expression that we have obtained.

Total

1.

Express the result in ro.

	1	320
	2⁄3	2131⁄3
	1⁄3	1062⁄3
\	1⁄6	531⁄3
\	1⁄11	291⁄11
\	1⁄22	141⁄21⁄22
\	1⁄66	42⁄31⁄61⁄66
Total		1012⁄31⁄111⁄221⁄66

Proof of the result as expressed in ro.

\	1	1012⁄31⁄111⁄221⁄66
\	2	2031⁄21⁄111⁄331⁄66
\	1⁄7	141⁄21⁄22
Total		320,

or 1 hekat.

It amounts in grain to ¹⁄₄¹⁄₁₆ hekat1²⁄₃¹⁄₁₁¹⁄₂₂¹⁄₆₆ro.