Illustrated Commentary on Nine Chapters, Vol. 1

When discussed in terms of the rough, the fractions are coarse; when discussed in terms of the fine, the fractions are subtle. Although they differ in coarseness and fineness, their actual value is the same. When multiple fractions are mixed and disordered, they cannot be combined unless they are made fine. Multiplying them to disperse them allows them to be combined. Generally, multiplying denominators with numerators is called "leveling" qi leveling/equalizing. Multiplying the denominators together is called "unifying" tong unifying/synchronizing. "Unifying" means to allow them to communicate and share a single denominator. "Leveling" means that the numerator and denominator are balanced in power, so as not to lose the original value. Fractions are gathered by kind, and things are grouped by number. Those with the same denominator are not far apart in value; those with different denominators are neither near nor far, yet those that form a whole body are followed and combined even if their positions differ. Those that are near but have different forms are treated as opposite even if they are in the same rank. Thus, the method of "leveling and unifying" is essential. When the complexity of numbers is manipulated, it becomes harmonious, much like using a pei-xi an ivory tool used for untying knots to untie a knot; there is no place where the principle does not hold. Multiply to disperse them, reduce to gather them, and use leveling and unifying to connect them. Is this not the guiding principle of calculation? As for this single method, one may also allow the denominator to divide the common denominator to form a rate, and then use that rate to multiply the numerator.

Follow this example

Commentary says

Place 3 and 5 the denominators in the right column, and 1 and 2 the numerators in the left column. Multiply the denominator 5 from the right column by the numerator 1 from the left column representing 1/3 to obtain 5.