Nine Chapters on Mathematical Art, Vol. 1

to serve as the divisor. Divide the dividend by the divisor to obtain the difference. We, Chunfeng and others, respectfully note: In this rule, multiplying the numerators by the opposing denominators and subtracting the smaller from the larger is the same as the method for subtraction. The only difference is that "Subtraction" seeks the remainder, while "Evaluating Fractions" seeks the difference by which one exceeds the other.

There is 1/3, 2/3, and 3/4. Question: If we reduce the larger and increase the smaller, what amount will equalize them?

Answer: Reduce 3/4 by 2, and 2/3 by 1, and add these to 1/3, so that each is equal to 7/12.

There is 1/2, 2/3, and 3/4. Question: If we reduce the larger and increase the smaller...