“Who would draw a picture to divide 2/3 by 3/4?” asked Marina Ratner, a professor emerita of mathematics at the University of California at Berkeley, in a recent Wall Street Journal opinion piece.

The array can be shown as 5 groups of 3 showing that 5 x 3 = 15. Or it could be shown as 3 groups of 5 showing that 3 x 5 = 15. This demonstrates that multiplication is commutative. Image caption, ...