Multiply Top and Bottom Until Exhausted

The general method of division|original: 除; chú is the exact opposite of multiplication|original: 乘; chéng. In multiplication, the product is obtained in the middle row; in division, the quotient|original: 得; dé is obtained in the top row.

Suppose 6 is the divisor|original: 法; fǎ and 100 is the dividend|original: 實; shí. When dividing 100 by 6, one should advance the divisor two places so that it sits directly under the hundreds place. In rod calculus, the divisor is moved along the board to align with the highest place value of the dividend. However, if you try to divide 1 by 6, the divisor is "many" while the dividend is "few," so it cannot be divided. Therefore, one must shift the divisor back to the tens place to divide the dividend. One says, "one times six," and by subtracting this from the hundred, forty remains; thus, it can be divided. The text describes the mental step of dividing 100 by 6: by placing the 6 under the tens place, the "one" in the quotient represents 10. $10 \times 6 = 60$, and $100 - 60 = 40$.

If the dividend is large and the divisor is small, one naturally stays at the hundreds place and does not shift back. Thus, for the stepping method|original: 步法; bùfǎ; the process of positioning rods, values of ten are placed in the tens position, and values of hundred are placed in the hundreds position.

If there is an empty space in the upper row, the divisor shifts back.

The remaining rules are all like those used during multiplication. If the dividend has a remainder, express it using the divisor: let the divisor be the denominator|original: 母; mǔ, literally "mother" and the remainder be the numerator|original: 子; zǐ, literally "son". This "mother and son" terminology for fractions remained standard in Chinese mathematics for centuries; a fraction was seen as a part (the son) supported by the whole (the mother).