Don't Skip the Last Step

The butterfly gives a correct answer, but rarely the tidiest one. Cross products often produce a fraction that can shrink, so finish every problem by simplifying to lowest terms — 14/24 becomes 7/12, and 26/48 becomes 13/24.

One more guard: the cross-product comparison tells you only which fraction is larger, not by how much. When you actually need the sum or difference, keep both numerators over the common denominator before you reduce.

Part of why the butterfly sticks is that it turns a multi-step rule into a single picture. Your memory holds shapes and patterns more easily than ordered procedures, so the crossing-wings image survives long after the formal steps fade. Draw it once on paper and the motion alone will remind you what to multiply.