Systematic Treatise on Arithmetic (1592) - Page 24

When the count reaches the ten-thousand place, stop. The position immediately ahead is the result in dan dan (石); a unit of dry measure, also known as a "stone" or "picul". Counting down sequentially, one arrives at the correct value.

Division by 10,000

Dividend 1,000 Start; Five-two doubled makes four At this position, add two to make four This is an abacus mnemonic for dividing by five. Since $2 \div 5 = 0.4$, the operator doubles the digit 2 to 4 and shifts the decimal place..

Lead Position 1,000


〇	〇	〇	〇
			Positioning
			Original Ten Start; call out "ten" going backward to determine the fit Result
		Hundred	As you count, when you meet the divisor's place at ten-thousand, stop.
	Thousand
	Ten-thousand The divisor above is 50,000 people; stop when reaching ten-thousand.
	The place immediately ahead is the result in dan.
Proof: This is the dan position; retreating and descending to smaller units gives: Dan	Dou dou (斗); 1/10 of a dan	Sheng sheng (升); 1/100 of a dan	He he (合); 1/1,000 of a dan

Restoration: Using Multiplication by Five

Four times five gives twenty This serves as the "check" for the previous problem: $0.0004 \times 50,000 = 20$..

Problem: Suppose you now have silver amounting to 265 taels tael (兩); the standard unit of silver weight, roughly 37 grams, 3 mace mace (錢); 1/10 of a tael, and 2 candareens candareen (分); 1/100 of a tael. This is to be divided among 6 people. Ask: how much does each...