《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§32. Division utilising a rate (4)

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

The relevant unit conversions for length are

\begin{aligned} 1 \unit{mile~(里)} &= 300 \unit{paces~(步)} \\ 1 \unit{pace~(步)} &= 6 \unit{rules~(尺)} \\ 1 \unit{rule~(尺)} &= 10 \unit{inches~(寸)}. \end{aligned}

See Vol. I §1 (Units of length).

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
今有九里渠、三寸魚、頭頭相次。問魚得幾何。 Suppose there be [a] nine-mile canal, [and] three-inch fishes, head [to] head next [after] each other. [We] ask, how many fishes result?
答曰、五萬四千。 Answer saith: five myriad [and] four thousand.
術曰、置九里、以三百步乘之、得二千七百步。 Method saith: put [down the] nine miles; multiplying it by three hundred paces, resulteth in two thousand seven hundred paces.
  • In modern notation, this is a conversion from miles to paces:
    9 \unit{miles} \times \frac{300 \unit{paces}}{\unit{mile}} = 2700 \unit{paces}.
又以六尺乘之、得一萬六千二百尺。 And multiplying it by six rules, resulteth in one myriad six thousand [and] two hundred rules.
  • Next we a conversion from paces to rules:
    2700 \unit{paces} \times \frac{6 \unit{rules}}{\unit{pace}} = 16200 \unit{rules}.
上十之、得一十六萬二千寸。 Decupling it upward, resulteth in sixteen myriad [and] two thousand inches.
  • Then we a conversion from rules to inches:
    16200 \unit{rules} \times \frac{10 \unit{inches}}{\unit{rule}} = 162000 \unit{inches}.
以魚三寸除之、即得。 Dividing it by [each] fish's three inches, [we] are done.
  • Finally we have the division determining the number of fish:
    \frac{162000 \unit{inches}}{3 \unit{inches} / {\unit{fish}}} = 54000 \unit{fish}.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §32". <https://yawnoc.github.io/sun-tzu/iii/32> Accessed yyyy-mm-dd.