Systematic Treatise on Arithmetic (1592) - Page 19

First Method: Initial division? Reading the Position 4 starts When encountering a four, carry twenty This is a mnemonic for division by two on the abacus: 4 divided by 2 equals 2. In the "Return Division" system, the quotient 2 is placed two columns to the left or "carried" as 20 in the chant. Remove the value from the current position and carry two to the left Dividend Hundreds starts Call out the hundreds place in order, then count back to the dan original: shi; a unit of volume for grain, approximately 100 liters Obtain Result: Two hundred four

Restoration: Using Multiplication by Two

original: Huanyuan yong er yin; "Restoration" is the process of checking a division result by multiplying it back by the divisor.

One times one is two; two times three is six; two times four is eight; two times two is four. These are simplified multiplication chants used to verify the previous calculation.

Suppose now we have silver amounting to 835 taels tael (liang); a traditional Chinese unit of weight for silver currency and 8 mace mace (qian); one-tenth of a tael. If each dan of rice costs 3 taels of silver, how much rice can be purchased?

The answer is: 278 dan and 6 dou dou; one-tenth of a dan, similar to a peck.

The method states: Set the total silver as the dividend dividend (shi); the number to be divided. Use the price of 3 taels per dan as the divisor divisor (fa); the number by which the dividend is divided 3 taels and apply Return Division original: Gui; refers to the "Nine Returns" division table, a set of mnemonics for abacus calculation. To determine the decimal place using the Positioning Method, simply identify the position one place before the taels as the dan units; move the result up and advance each place in order to obtain the correct value.

Method: Return Division by three

The following are the key technical terms used in this lesson:
Restoration Huanyuan; the process of multiplying the quotient by the divisor to verify the original dividend, Multiplication by Two Er yin; a specific verification step, Purchasing Rice Dimi; a standard word problem category in Chinese mathematics, Dividend Shi; the total amount being divided, Divisor Fa; the rate or unit price used to divide, Return Division Gui; division performed using traditional abacus chants, Positioning Method Dingwei fa; the rule for determining the unit (e.g., hundreds, tens, or ones) of the result.