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CHAPTER I—EGYPTIAN ARITHMETIC
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Assume 1. Multiplying by the given expression we have
| 1 | 1 | |
| 2 | 2 | |
| 1⁄3 | 1⁄3 | |
| 1⁄3 of 1⁄3 | 1⁄9 | |
| 1⁄9 | 1⁄9 | |
| Total | 31⁄21⁄18 | |
Get 1 by operating on 31⁄21⁄18
| 1 | 31⁄21⁄18 | |
| 1⁄2 | 11⁄21⁄41⁄36 | |
| \ | 1⁄4 | 1⁄21⁄41⁄81⁄72 |
| 1⁄8 | 1⁄41⁄81⁄161⁄144 | |
| 1⁄16 | 1⁄81⁄161⁄321⁄288 | |
| \ | 1⁄32 | 1⁄161⁄321⁄641⁄576 |
The total, 1⁄41⁄32, times, 31⁄21⁄18 makes 1, for we have first to add 1⁄2,1⁄4, and 1⁄8, and then the smaller fractions
1⁄721⁄161⁄321⁄641⁄576
which, taken as parts of 576, make
8361891,
a total of 72, or 1⁄8 of 576. Therefore the answer is 1⁄41⁄32.
Proof.'
| 1 | 1⁄41⁄32 | |
| 2 | 1⁄81⁄16 | |
| 1⁄3 | 1⁄121⁄96 | |
| 1⁄3 of 1⁄3 | 1⁄361⁄288 | |
| 1⁄9 | 1⁄361⁄288 |
The total is 1, for we have first to add 1⁄2 and 1⁄4, and then the smaller fractions
1⁄321⁄161⁄121⁄961⁄361⁄2881⁄361⁄288
which, taken as parts of 288, make
9182438181,
a total of 72, or 1⁄4 of 288.
Express the result in ro.
| 1 | 320 | |
| 1⁄2 | 160 | |
| \ | 1⁄4 | 80 |
| 1⁄8 | 40 | |
| 1⁄16 | 20 | |
| \ | 1⁄32 | 10 |
| Total | 90. | |
