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### Negative 5 and Minus 5

```Date: 10/05/2002 at 13:06:27
From: Math
Subject: Difference between negative five and minus five

Can you tell me the difference between negative five and minus five?
When should I use negative? When should I use minus?

If I have a lot of numbers, e.g. +3 ,-7, -3/4, -5.4, 1/4.......

Thank you!
```

```
Date: 10/05/2002 at 16:24:26
From: Doctor Achilles
Subject: Re: Difference between negative five and minus five

Hi,

Thanks for writing to Dr. Math. That's a very good question. It's
very easy to get negative 5 and minus 5 confused because people often
say "minus 5" when they should actually say "negative 5."

I'm going to answer this in a sort of roundabout way that I hope will
help get the point across.

A long, long time ago, people thought only in terms of the natural
numbers:

1, 2, 3, 4, 5, ...

You can do a lot with the natural numbers. You can count how many
sheep, dollars, children, and friends you have. You can count how many
apples you have. You can even do simple arithmetic: if you have 6
apples and you lose half (divided by 2), you end up with 3 apples; if
you have 6 apples and you double the number (times 2), you end up with
12 apples; if you have 6 apples and you get two more (plus 2), you
have 8; if you have 6 apples and you lose two (minus 2), you have 4.

The idea of subtraction (or minus) has been around since the days
before fractions and integers, when people only thought in natural
numbers.

If I say "nine, five" to you, all I have done is list two numbers:

9, 5

I haven't told you anything about what to do with those numbers. The
most you can do is just remember them. You don't know whether I want
you to multiply them, divide them, add them, or just remember both of
them (one could be the number of oranges I have and the other the
number of cousins I have).

If I say "nine plus five" to you, then I have told you to add two
numbers. You don't have to remember 9 and 5, you just have to know

Somewhere along the line, some people came up with zero (and that was
a big deal) and some other people came up with fractions (and that was
a big deal). Then some other people came up with integers. Integers
are all the positive (natural) numbers, and zero, and the negative
numbers:

..., -3, -2, -1, 0, 1, 2, 3, ...

It's hard to think of apples and sheep in terms of negative numbers,
but they are useful in thinking about money and other things. For
example, right now, my bank account has a negative amount of money in
it.

Negative numbers are just a kind of number, not really any different
from positive numbers.

If I say "nine negative five" to you, all I have done is list two
numbers:

9, -5

I haven't told you anything about what to do with those numbers. The
most you can do is just remember them. You don't know whether I want
you to multiply them, divide them, add them, or just remember both of
them (one could be the balance in my friend's bank account and the
other the balance in my bank account).

If I say "nine minus five" to you, then I have told you to subtract 5
from 9. You don't have to remember 9 and 5, you just have to know that

So "negative 5" is a number and "minus 5" is a mathematical operation
you can do to another number. If it helps, you can think of "negative
5" as a noun, as in the sentence "negative 5 is my least favorite
number"; and you can think of "minus 5" as a verb as in the
(ungrammatical) sentence "I want you to take 9 and minus 5 it."

One other thing. This tends to get complicated when you start doing
crazy things like:

"negative 5 plus 6"
or
"8 minus negative 5"

If you want, you can check out this page for my suggestions of how to
deal with this:

Tips for Negative and Positive Numbers
http://mathforum.org/library/drmath/view/57873.html

I should note that I'm a bit sloppy with the distinction between
"minus" and "negative" on that page.

For the last part of your question, the list you gave reads:

"positive three" OR "three"
"negative seven"
"negative three-fourths"
"negative five point four"
"one fourth" OR "one quarter"

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

```
Date: 10/06/2002 at 02:58:25
From: Math
Subject: Thank you (Difference between negative five and minus five)

Dear Dr. Math,

Mathematics_. It says "Weather-forecaster: The temperature fell to
'minus five degrees'." Is it right?

Thank you.
Best regards!
```

```
Date: 10/06/2002 at 05:51:07
From: Doctor Achilles
Subject: Re: Thank you (Difference between negative five and minus
five)

In English it is not uncommon to hear "negative 5" called "minus 5."
This is technically incorrect, but if you're not speaking with
mathematicians, then it's acceptable to just use "minus 5."

else.

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Subtraction
Middle School Negative Numbers

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