Nine Chapters on Mathematical Art, Vol. 1

Answer: 4/9 of a square bu

Multiplying Fractions

We, Chunfeng and others, respectfully note: "Multiplying fractions" means multiplying the denominators to form the divisor, and multiplying the numerators to form the dividend. Hence it is called Multiplying Fractions.

Procedure: Multiply the denominators to form the divisor. Multiply the numerators to form the dividend. Divide the dividend by the divisor to obtain the result.
Whenever the dividend does not fully fill the divisor, there exist names for the numerator and denominator. If there is a number used to multiply the dividend and increase it, it will eventually fill the divisor and become a whole number.
Furthermore, since the numerator has a multiplier, the denominator must be divided back accordingly. "Dividing back" means dividing the dividend by the divisor. Now, if the numerators are multiplied, the denominators must each be divided back. Dividing them accordingly means letting the denominators multiply each other and then dividing consecutively. This field has width and length; it is difficult to explain using only width. If there is an inquirer who asks: "Two horses are worth 12 jin of gold. Now selling 12 and 2/3 horses, how much does the person receive?" Answer: 80 and 2/3 jin of gold. If two people divide this, what should be done? Use the standard division procedure: use 12 jin of gold as the dividend, and 3 and 1/3 people as the divisor. Suppose the question is changed to: "50 horses are worth 3 jin of gold. Now selling 4 and 2/7 horses, how much does the person receive?" Answer: Each person receives 2/35 of a jin. For the person who does this, one should equalize the gold and the number of people; both will match the initial question.