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### 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/
```
Associated Topics:
Elementary Subtraction
Middle School Negative Numbers

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