Page:The Rhind Mathematical Papyrus, Volume I.pdf/94

Express the result in ro

	1	320
	1⁄10	32
	1⁄5	64
	Total	96.

Proof of the result as expressed in ro.

	1	96
	2	192
	1⁄3	32
	Total	320.

Expressed in "Horus eye" fractions^[1] it makes of grain ¹⁄₄¹⁄₃₂¹⁄₆₄ hekat 1 ro.

Proof of the result expressed in this form.

	1	1⁄41⁄321⁄64	hekat	1	ro
	2	1⁄21⁄161⁄32	"	2	"
	1⁄3	1⁄161⁄32	"	2	""
	Total	1.

Problem 36
I have gone in three times, my ¹⁄₃ and my ¹⁄₅ have been added to me, and I return having filled the measure. What is the quantity that says this?

Assume 1. Multiplying by 3¹⁄₃¹⁄₅, we have

	1	1
	1	1
	1	1
	1⁄3	1⁄3
	1⁄5	1⁄5
	Total	31⁄31⁄5

Get 1 by operating on 3¹⁄₃¹⁄₅. Apply this to 30; it makes 106. Multiply 106 so as to get 30.

	1	106
	1⁄2	53
\	1⁄4	261⁄2
\	1⁄106	1
\	2
\	1⁄2
	Total	30.

1. See Introduction, page 31. The "Horus eye" fractions are indicated by black-faced type throughout this Work.