"user" <firstname.lastname@example.org> writes: >I use A = 4*2 to find area of a 4" 2" rectangle, and my >answer is supposed to be 8^2 (64?); Is that to say there >are 64 little units of the given measurement in my rectangle?
You are confusing two things: the numeric computation and the units of the result.
You are multiplying (4 inches) by (2 inches). The numeric part of the result is 4*2=8. The unit part is inches*inches = square inches.
Computation with units is >>>> analogous to <<<< (not the same as) computation with variables.
4x + 2x = 6x 4 in + 2 in = 6 in 4x * 2x = 8x^2 4 in * 2 in = 8 in^2
(An inch-pound is a unit of energy, if I'm remembering my physics correctly. You don't see inch-pounds in practical computation very often, but foot-pounds are more commonly used.)
I'm emphasizing "analogous to" because you shouldn't get the idea that a unit is a quantity, in the way that a variable represents a (perhaps unknown) quantity. So, for example, 4x+2y is a perfectly valid expression, just one that can't be simplified unless we learn something about the values of x and y. But 4 in + 2 lb is just plain wrong -- it's never meaningful to add inches and pounds.