Systematic Treatise on Arithmetic

Answer: The total amount due is 70 taels original: 兩 (liǎng); a unit of silver currency weight, 3 mace original: 錢 (qián); 1/10th of a tael, and 5 candareens original: 分 (fēn); 1/100th of a tael of silver.

The method states: Set the total amount of rice as the Dividend original: 實 (shí); the quantity to be operated upon and the unit price as the Multiplier original: 法 (fǎ); multiply them together.

Positioning the Decimal: First, count from the original dividend starting at the hundreds place and move down until you reach the "stone" unit. The position one place below the stone is the place for the mace. Then, count backwards and shift the digits upward to reach the correct total.

The original multiplier is used.

The Dividend begins the call: In abacus calculation, "calling" refers to reciting the rhythmic mnemonics used to move the beads.
Three, one, fifteen Change 5 to 1 Add 5 to the position below
Five, one, twelve Change 4 to 1 Add 2 to the position below
Three, one
Three becomes nine Remove from this position Add 9 to the position below
Two becomes six Remove from this position Add 6 to the position below

A calculation diagram for the abacus or counting rods. It features circular markers indicating place values: "Hundred" (百), "Ten" (十), and "Stone" (石 - a unit of rice volume). It also identifies the "Dividend" (實) and the "Head" (首) and "Tail" (尾) of the numerical sequence, guiding the user on where to start and end the calculation.

Positioning the Decimal: This refers to the mace; move back and shift the values upward to get the correct total.
The multiplier used above is 3 mace per stone. When the calculation reaches the "stone" unit, stop; the position immediately below it is the mace.

Restoration: Use the "Division by Three" rule. The method is detailed later. Restoration is the practice of performing the inverse operation—in this case, division—to prove the multiplication was correct.

Vocabulary Reference:

• Silver (銀): The medium of exchange.
• Tael (兩), Mace (錢), Candareen (分): The denominations of silver by weight.
• Dividend (實): The number being multiplied or divided.
• Multiplier/Divisor (法): The factor being applied.
• Positioning (定位): The crucial process of determining where the decimal point (or unit place) falls on the abacus.
• Division Rule (歸): A specific set of abacus rhymes used for division.
• Stone (石): A traditional unit of dry volume for grain, roughly equal to 100 liters.