《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§9. Multiplication determining a total (3)

This section gives a word problem where multiplication is used to determine a total.

The relevant unit conversion for weight is

1 \unit{catty~(斤)} = 16 \unit{taels~(兩)}.

See Vol. I §2 (Units of weight).

Translation

Chinese source text: Version A, Version C, Version D. (This section is missing in Version B.)
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
今有三萬六千四百五十四戶、戶輸綿二斤八兩。問計幾何。 Suppose there be three myriad six thousand four hundred [and] fifty-four households, [each] household contributing silk-floss two catties [and] eight taels. [We] ask, how much amounteth [this] to?
答曰、九萬一千一百三十五斤。 Answer saith: nine myriad one thousand one hundred [and] thirty-five catties.
術曰、置三萬六千四百五十四戶、上十之、得三十六萬四千五百四十。 Method saith: put [down the] three myriad six thousand four hundred [and] fifty-four households; decupling it upward, resulteth in thirty-six myriad four thousand five hundred [and] forty.
以四乘之、得一百四十五萬八千一百六十兩。 Multiplying it by four, resulteth in one hundred [and] forty-five myriad eight thousand one hundred [and] sixty taels.
以十六除之、即得。 Dividing it by sixteen, [we] are done.
  • The awkward presentation is due to 1 catty (斤) being 16 taels (兩). In modern notation, each household contributes
    \begin{aligned} 2 \unit{catties} + 8 \unit{taels} &= (2 \times 16 + 8) \unit{taels} \\ &= 40 \unit{taels} \\ &= 10 \times 4 \unit{taels}, \end{aligned}
    and hence the total amount is
    36454 \unit{households} \times \frac{10 \times 4 \unit{taels}}{\unit{household}} \div \frac{16 \unit{taels}}{\unit{catty}} = 91135 \unit{catties}.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §9". <https://yawnoc.github.io/sun-tzu/iii/9> Accessed yyyy-mm-dd.