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Re: Square feet
Posted:
Nov 29, 2004 3:36 PM
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"user" <user@domain.ok> 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
4x + 2y = can't simplify 4 in + 2 lb = can't add
4x * 2y = 8xy 4 in * 2 lb = 8 in-lb
(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.
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