Negative Number or Subtraction?

Date: 12/16/2003 at 12:29:42
From: Andrea 
Subject: Minus sign or subtraction?

When I see a '-' in front of a number, e.g., in 

  2(5-6-3)-8 

how can I tell whether it's supposed to indicate a negative number, or
a subtraction? 

Date: 12/16/2003 at 13:17:06
From: Doctor Peterson
Subject: Re: Minus sign or subtraction?

Hi, Andrea.

If it's between two numbers, it tells you to subtract; if what's 
before it is not a number (or something equal to a number, like a 
parenthesized expression), then all you can do is take the negative 
of what comes after. In other words, a "-" is only to be interpreted 
as a negative when there is no way to take it as a subtraction.

For example,

  2-3      says to subtract 3 from 2, NOT to multiply 2 by -3.

  2(-3)    says to take the negative of 3 and multiply by 2, because
           you have to evaluate the expression -3 inside the
           parentheses first.

  (1+1)-3  says to add 1 and 1, then subtract 3 from the result.

  2-(1+2)  says to add 1 and 2, then subtract that number from 2.

  -(2+3)   says to add 2 and 3, then take the negative of the result.

  2--3     says to take the negative of 3, then subtract that from 2.

           (Some people would require you to write this as 2-(-3), 
           but there's only one way to interpret it anyway, since 
           the second "-" does not follow a number.)

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/