What are some of the ways in which one can motivate the multiplication of real numbers?
The sum of two real numbers can be thought in terms of jumps along a horizontal line. For example, (3)+(-2) may be "interpreted" as follows: initially "a thing" is sitting down over number 3 and then it jumps two unities to the left; it falls over number 1.
Do you know of a similar way to "think of" the multiplication of reals numbers?
Even though the multiplication can be thought as a short way to express certain sums (for example, 5*3 is just another way of saying 5+5+5), I am looking forward to reading 'bout geometric ways to motivate or introduce the operation.
Do you know if a connection with smilar triangles can or has been established once?
Please, forgive me in advance for the vagueness and/or naïveté of this question of mine.