Systematic Treatise on Arithmetic: Volume 2

Suppose there are currently 1,345,679 soldiers. Each soldier is given 8 dou dou: a traditional unit of dry volume, approximately 10 liters. There are 10 dou in 1 shi. of rice. Question: What is the total amount of rice required?

Answer: 1,076,543 shi shi: often called a "stone," the standard large unit for measuring grain. and 2 dou

Method: Set the number of soldiers as the multiplicand shi: the base number to be multiplied. Set the 8 dou of rice given per person as the multiplier fa: the factor used to multiply the base number. Multiply them to find the answer.

Multiplier [Method] ◯ Multiply

A mathematical diagram illustrating the "yin" multiplication method (single-digit multiplication) on an abacus or counting board. - The top row contains markers for the Multiplicand and the "Tail" (the last digit of the number). - The middle section shows the step-by-step process of replacing digits on the abacus rods. For example, when multiplying by 8, a "9" on a rod is replaced by the first digit of the product (7), and the second digit (2) is added to the rod to the right. - The bottom row indicates decimal positioning for units like "hundreds," "tens," and "individual soldiers." - Annotations explain how to shift the decimal point when dealing with the "dou" unit. Multiplicand ◯ Tail 〼 original: 尾. Refers to the last digit of the number being processed. Start the Call original: 起呼. The act of reciting the multiplication table aloud while moving beads. 8 times 9 is 72 Change 9 to 7; add 2 to the lower place original: 變九爲七下位加二. On the abacus rod where the 9 was, it is replaced with a 7, and a 2 is added to the rod to the immediate right. 〼 8 times 7 is 56 Change 7 to 5; add 6 to the lower place 〼 8 times 6 is 48 Change 6 to 4; add 8 to the lower place Determining the Decimal Position Since the unit is dou, move the position forward one place to obtain the correct result. Above the multiplier is "8 dou per person." When you encounter the unit of "person," set the position one place below it as the dou unit.

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