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[Phys-L] Re: Calculators a Distraction?



John Barrer wrote:
Is it ever pointed out in primary grades that
multiplication is a short-cut for addition while
division is a short cut for subtraction?

I sure hope not.

Iterated addition gives you a*b.
Iterated subtraction gives you -a*b ... not a/b.

Yes, I know the corners and *three* edges of the following
graph:

multiplication <--(iteration)-- addition
| |
(inverse op) (inverse op)
| |
division subtraction

But it does not follow that we can fill in the fourth
side with "iteration". Iteration and inversion do not
compose so simply.

Yes, I suppose there is some tortured interpretation
under which division is iterated subtraction ... but
it is not parallel to iterated addition, and has no
pedagogical value.