Nine Chapters on Mathematical Art, Vol. 1

Because the denominator used to designate the fraction enters into the calculation, it must be removed. Therefore, now the denominators are multiplied to form the divisor and divided consecutively.

Now there is a triangular field gui tian literally "triangular field", 12 bu wide, and 21 bu long. Ask: What is the area of the field?

Answer: 126 bu

There is another triangular field, 5 and 1/2 bu wide and 8 and 2/3 bu long. Ask: What is the area of the field?

Answer: 23 and 5/6 bu

Procedure: Take half of the width to multiply the length. Taking half the width compensates for the deficiency with the excess, making it a rectangular field. One can also take half the length to multiply the width. Note: multiplying the width by the length takes the average flat number, so multiplying the width and length forms the product; divide by the mu-method to obtain it.