Computation is all about shortcuts.
Consider, for example, how you would compute 4 ∗ 5.1
A reasonable response would be ìI donít ëcomputeí anything. I simply
recall a fact I have memorized: 4 ∗ 5 = 20.î
Indeed, that is how almost all of us arrive at that answer now, but
consider how we got to this point historically. That 4 ∗ 5 is a shortcut
notation for adding four 5s, that is, 4 ∗ 5 = 5 + 5 + 5 + 5 (or equivalently
five 4s), and multiplication of whole numbers in general is simply shortcut
addition.
Thus we could solve the original exercise 4 ∗ 5 by adding four 5s,
again applying memorized ìfactsî: 5 + 5 = 10, 10 + 5 = 15, and finally
15 + 5 = 20, to arrive at our final answer.