Area model

An area model draws a fraction of a square. Split a unit square into equal columns and rows; a rectangle that is a/b of the width and c/d of the height covers a/b × c/d of the square.

That makes fraction multiplication something you can see. Read the same picture backwards and it shows division: fix the area and one side, and the missing side is the quotient. A rectangle with area 2/3 and height 3/4 has width 8/9, so 2/3 ÷ 3/4 = 8/9. The width is the missing factor, because 8/9 × 3/4 = 2/3. Rearranged, that is 2/3 × 4/3 = 8/9, the reciprocal rule.