《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§7. Division utilising a rate (2)

This section gives a word problem where division by a rate is used to determine an amount.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
今有丁九萬八千七百六十六、凡二十五丁出一兵。問兵幾何。 Suppose there be males nine myriad eight thousand seven hundred [and] sixty-six, [and] every twenty-five males [we] send forth one soldier. [We] ask, how many [be the] soldiers?
答曰、三千九百五十人奇一十六丁。 Answer saith: three thousand nine hundred [and] fifty people remainder sixteen males.
術曰、置丁九萬八千七百六十六為實、以二十五為法。實如法、即得。 Method saith: put [down the] males nine myriad eight thousand seven hundred [and] sixty-six as [the] dividend, [and] use twenty-five as [the] divisor. [Taking the] dividend as [per the] divisor, [we] are done.
  • In modern notation,
    \frac{98766 \unit{males}}{25 \unit{males} / {\unit{soldier}}} = 3950 \unit{soldiers} + \frac{16 \unit{males}}{25 \unit{males} / {\unit{soldier}}}.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §7". <https://yawnoc.github.io/sun-tzu/iii/7> Accessed yyyy-mm-dd.