Let a/b and c/d be the two fractions. I'm going to put "?" to represent the unknown comparison. a/b ? c/d Multiply a/b by d/d, and c/d by b/b: ad/bd ? bc/bd Multiply both sides by bd: ad ? bc That's it. But using the video as an example: 3/5 ? 4/7 (3x7)/(5x7) ? (4x5)/(5x7) 21/35 ? 20/35 21 ? 20 21 > 20 Therefore, 3/5 > 4/7