Systematic Treatise on Arithmetic

Subtract the smaller from the larger; the remainder, 40, is the Constant Divisor (常法): a fixed value used in the final division step of the algorithm. ○ Additionally, take the middle-right 7 and multiply by the lower-left 1 [thousand] original: 九百九十六千九百. This appears to be a transcription of the total cash (999) and total fruits (1,000) mentioned on the previous page.... Furthermore, take the middle-left 4 and mutually multiply (互乘) by the lower-right 1,000 to get...

...19 cash, which results in 93 cash 9 thousand. Subtract the smaller from the larger to get a remainder of 9,300 cash, then divide this by the Constant Divisor to obtain 30, which is the Short Divisor (短法): a secondary operational value in this specific method.

If seeking the quantity of sweet fruits: multiply 70 by 9 to get 630 sweet fruits. Alternatively, multiply 70 by 1...

...11 cash to get 870 The arithmetic here follows a specific proportional rule; the text describes how to arrive at the final counts for each fruit type. sweet fruits. Now, subtract 630 from the total number of fruits to find a remainder of 240 bitter fruits. Further, subtract the price of the sweet fruits from the total money to find the remaining money for the bitter fruits. This matches the inquiry.

Song of Distributing Salt across Boats

Four thousand, three hundred and fifty [units of] salt;
Large and small boats must be handled in equal proportion original: 齊肩 (side-by-side/equal shoulder), meaning the distribution must be balanced across the different capacities..
Five hundred [units of] salt are loaded onto three large vessels;
Three hundred [units of] salt are loaded onto four small boats.
I ask of you: what is the number of boats for each?
And how many yin (引): a traditional Chinese unit of weight used specifically for salt, roughly equivalent to 100 catties or 60 kilograms of salt does each boat carry?