Systematic Guide to Computational Methods, Volume 14

Zhang: 108 ounces Li: 36 ounces Combined total: 144. This is the divisor. Separately, take the woven cloth (72 feet) and multiply by Zhang’s 108 ounces to get Zhang’s dividend: 7,776. Multiply by Li’s 36 ounces to get Li’s dividend: 2,592.

Set each product as the dividend and divide by the divisor to find the solution.

The Mnemonic Song
Mathematical problems were often written as poems to help students memorize the scenario and the necessary values.
Sister Zhao boasts she spins hemp with great speed,
The Li and Zhang houses hired her for their need.
The Li family gave six catties and twelve ounces of fiber,
While two catties and four from Zhang went to the weaver.
Seventy-two feet of cloth was produced by her hand,
But now the two parties are brawling across the land!
I ask of you, scholars skilled in the calculating art,
How should we divide it so each gets their fair part?

Answer: The Zhang residence receives 5 zhang and 4 feet. The Li residence receives 1 zhang and 8 feet.
In this period, 1 zhang = 10 feet (chi). Therefore, the Zhang family receives 54 feet and the Li family receives 18 feet.

Method: Set the total woven cloth of 72 feet as the dividend original: "實" (shí), the number to be divided.. Combine the two portions of hemp: For Zhang, 6 catties and 12 ounces converting catties to ounces by multiplying by 16 and adding the remainder equals 108 ounces. For Li, 2 catties and 4 ounces equals 36 ounces. The total of 144 ounces serves as the divisor original: "法" (fǎ), the number used to divide the dividend..