Algorithm for Unifying Computing: Volume II

Answer: 18 taels, 3 mace, 7 candareens, 5 cash These are traditional Chinese units of weight and currency. 1 Tael (兩, liang) contains 10 Mace (錢, qian); 1 Mace contains 10 Candareens (分, fen); 1 Candareen contains 10 Cash (厘, li).

Method: Set the total amount of hemp as the dividend dividend (shi); the number to be divided. Using the rate of four [units of] hemp sold per mace as the divisor divisor (fa); the number by which another is divided, perform the division to obtain the answer.

The Positioning Method: Identify the position one place ahead of the catty catty (jin); a unit of weight roughly equal to 600 grams to fix the "mace" position. From there, advance in reverse order to obtain the result.

Division Method

Four-two, change to five Change 2 to 5 This mnemonic represents $2 \div 4 = 0.5$. On the abacus, the bead for 2 is replaced with a 5.

Four-three, seventy-two Change 3 to 7 and add 2 to the position on the right This represents $3 \div 4 = 0.75$. On the abacus, the 3 is replaced by 7, and 2 beads are added to the next rod to the right.

Meeting four, carry ten Remove 4 from the base position and carry 1 to the left This represents $4 \div 4 = 1$. The 4 is cleared, and 1 is added to the rod to the left.

Four-one, twenty-two Change 1 to 2 and add 2 to the position on the right This represents $1 \div 4 = 0.25$. The 1 is replaced by 2, and 2 is added to the next rod.

Meeting four, carry ten Remove 4 from the base position and carry 1 to the left

Four-three, seventy-two Change 3 to 7 and add 2 to the position on the right

Meeting four, carry ten Remove 4 from the base position and carry 1 to the left

Positioning The top [of the calculation] is 4 catties; stop when you encounter the catty. One position ahead yields the "mace." Since it is the mace, advance in reverse order. The result is obtained. Original Calculation Calling the hundreds, move backward. Count sequentially until you reach the catty.

Restoration: Use multiplication by four This refers to checking the division by performing the inverse operation—multiplying the quotient by the divisor to see if it returns the original dividend.