Nine Chapters on Mathematical Art, Vol. 1

the numerical values, they ultimately reach the same result. The method for numerator and denominator pushes one another, and there are discrepancies. Therefore, those who practice this method first manage the various fractions.

The method states: If it can be halved, halve it. If it cannot be halved, set aside the numerator and denominator numbers. Subtract the smaller from the larger, and continue to subtract to find their common factor. Use the common factor to reduce it. Using the common factor to reduce is division. The reason for subtracting is that all are overlays of the common factor, so reducing by the common factor is used.

Now, there is 1/3 and 2/5. How much is the total?
Answer: 11/15.

There is also 2/3, 4/7, and 5/9. How much is the total?
Answer: 1 and 50/63.

A woodblock print illustration of mathematical notation for fraction arithmetic.