Systematic Treatise on Arithmetic

How much total grain results from this?

The method is as follows: Place the silver amount on the left as the Dividend original: 實 (shí); the number to be operated upon. Use the rate of two stones original: 石 (dàn); a unit of volume for grain of grain for every tael of silver on the right as the Multiplier original: 法 (fǎ); the constant rate. Multiply them to find the answer.

Regarding the Rule of Positioning The system for determining decimal places on the abacus: Simply identify the position one place below the taels original: 兩 (liǎng); the primary unit of silver which is the position of the mace and designate that as the position for "stones." Moving one place higher which is the tael position designates "ten-stone" units. Moving up another place the ten-taels position designates "hundred-stone" units. This yields the correct total.

This is what is called "multiplication where both figures push toward the lower positions." First, count from the hundreds place of the original Dividend downward to the taels. When you encounter the first digit of the Multiplier—the rate of two stones per tael—then the result is obtained in the lower positions. This method does not move forward, but rather counts backwards and upwards through each position to determine the magnitude of the result.

The method for arranging the calculation is laid out below: