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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.......
How to read them?

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 
that the answer is 14.

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 
the answer is 4.

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"

Hope this helps.  If you have other questions about this or anything 
else, please write back.

- 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,

I think your answers are great help to me. Thanks again.

Can you answer another question? I'm reading a book called _Exploring 
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."

Hope this helps.  Please write back if I can help you with anything 
else.

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

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