Nine Chapters on Mathematical Art, Vol. 1

When denominators are the same, they share a common base. When they are different, we balance the numerators and denominators so that their original values remain unchanged, just as objects are grouped by type or gathered in herds.

Multiplying the numerators to express them in broader terms or using reduction to express them in finer terms changes the appearance, but the actual value remains the same. When multiple fractions are mixed, they cannot be combined unless they are refined. We use multiplication to distribute them, and once they are distributed, they can be added together. In general, multiplying the numerators by the opposing denominators is called "balancing" (qi), and multiplying the denominators by one another is called...

The Rule states: Multiply the numerators by the opposing denominators, then add them together to serve as the dividend (shi). Multiply the denominators together to serve as the divisor (fa).

Opposing denominators

Combining Fractions

We, Chunfeng and others, respectfully note: The method for combining fractions is not limited to a single approach. Because the numerators and denominators are disparate and the denominators vary, the rough and the fine are already distinct. It is difficult to follow a single principle. Therefore, we balance the various fractions and unify their denominators so they can be combined. Thus, this is called "Combining Fractions."

Answer: 43/60

Question: When these are combined, what is the total?

There is also 1/2, 2/3, 3/4, and 4/5.