I like to address this question about multiplying two negative numbers by
examining what we mean by the following questions:
"You buy 5 books priced at $10 each. How much did you spend?" Most students
will readily agree that this asks for the calculation (5 books) x (-$10)
= -$50. The book price and the total cost are negative numbers because they
represent expenses. The number of books is positive because the buyer is
receiving the books while spending the money.
Now what about the opposite statement:
"You sell 5 books priced at $10 each. How much did you earn?" Note that the
book price remains the same (negative $10!), so changing "buy" to its
opposite "sell" introduces a second negative sign. The number of books is
now negative since the seller is giving up the books. Thus we have the
calculation
(-5 books) x (-$10) = +$50. We know the result must be positive because it
represents income. Most people will automatically change the double
negatives and only write 5 x 10 = 50. This verifies that the product of two
negative numbers must be positive in a common sense argument that students
find convincing.
George Alexander
University of Wisconsin Colleges
Developmental Math Coordinator
UW Rock County
2909 Kellogg Ave.
Janesville, WI 53546-5699
(608) 758-6627
-----Original Message-----
From: owner-mathedcc@archives.math.utk.edu
[mailto:owner-mathedcc@archives.math.utk.edu]On Behalf Of Phil Mahler
Sent: Sunday, November 07, 1999 4:13 PM
To: mathedcc@archives.math.utk.edu
Subject: [MATHEDCC] Marilyn Vos Savant
>From today's Newspaper in the Ask Marilyn, Marilyn vos Savant column. Nice
to see this in the popular press - that's more important than the actual
question.
Of course maybe someone has a better answer to Sandy's original question.
Phil Mahler
Middlesex CC
Springs Road
Bedford, MA
Here's a question from my 83 fifth-grade math students, who keep asking me
what your answer is: "in real life, when would you ever multiply (or
divide, for that matter) two negative numbers?" The closest I've come up
with is, "if you didn't get what you didn't want, that's positive."
-Sandy Hindy, Westlake Village, Calif.
Forget this kind of justification for studying math. It's as irrelevant as
asking a question like, "In real life, when would you ever do a sit-up?"
Unless you work as a trainer, you wouldn't. That doesn't mean you should
complain about doing sit-ups as part of physical conditioning.
People need to be in good intellectual condition too. Even if you're not
going to make heavy use of math in your profession, you still need to know
how to think logically. Tell the kids I said that studying math
accomplishes two goals: It prepares some kids to think like scientists,
and it prepares all the rest of them to think, period.
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