Systematic Treatise on Arithmetic (1592) - Page 5

General Source of Algorithmic Methods, Volume 2

This is what is called the rule of "treating the position as double whenever one is encountered." This refers to a specific multiplication mnemonic where each unit is doubled, effectively shifting its value and position on the abacus.

End Position of the Dividend			Position of the Product
Start Begin the verbal mnemonic	Peck	Liter	Hundred
2 becomes 8	3 becomes 6	2 becomes 4	1 becomes 2
Subtract 8 from this position	Subtract 6 from this position	Subtract 4 from this position	Subtract 2 from this position
Add 8 to the position below	Add 6 to the position below	Add 4 to the position below	Add 2 to the position below

This refers to the "stone" unit; by moving forward and linking the numbers, elevate each position to find the total. On the Multiplier line, for every tael original: 兩 (liǎng) there are two stones original: 石 (dàn); stop when you reach the tael position. One place lower than that marks the position on the abacus for the stones. Position for Bolts The character 疋 (pǐ) usually refers to bolts of cloth; here it is used to designate a specific decimal place in the layout.

Bolt Original value
Tael Multiplier
Ten
Hundred Begin the call at the hundred position and count down to the taels

Result:
Hundred
Forty
Stone
Peck

Restoration Performing the inverse operation to check the math.
Use the "Rule of Two-Reduction," detailed later:

When meeting two, advance one to the tens original: 逢二進一十; this is a standard abacus division mnemonic where 2 ÷ 2 = 1, shifting the result one place higher.
When meeting four, advance twenty
When meeting six, advance thirty
When meeting eight, advance forty

Suppose now there are 234 stones and 5 pecks of rice. Each stone is sold for 2 mace original: 錢 (qián); 0.2 taels of silver. How much silver is owed in total?