Associated Topics || Dr. Math Home || Search Dr. Math

### 91 - 92 = ?

```
Date: 01/23/97 at 22:54:40
From: Garry Griffin
Subject: 91-92

91 - 92 = ?
```

```
Date: 01/26/97 at 16:23:18
From: Doctor Reno
Subject: Re: 91-92

Hi Garry!

I assume that you are asking how to subtract a number from a number
that is smaller than itself. My students don't think they understand
this either! Please notice that I wrote *think*!

I live in New England, and last weekend it was extremely cold here. In
fact, the temperature dropped to below zero! One night, the
temperature was -5 degrees! Pretty nasty out!

I mention this to demonstrate to you that you do, indeed, understand
how to do the subtraction in your problem...and I will prove it to
you!

Think of a thermometer....and of an unusual, *very* unusual, winter
day. On this strange day, the temperature outside rises to a very hot
91 degrees. You and your friends put on your shorts and turn on the
air conditioning!  You look at the thermometer and notice that the red
mercury inside it has risen up to the mark that says 91.

But during this day, clouds roll in and it starts cooling off *very*
quickly. This is historic weather that you will tell your
grandchildren about, so you spend lots of your time on this day
watching the mercury drop in your thermometer. After the temperature
has dropped 10 degrees, the thermometer reads 81; after a 25 degree
drop, the thermometer reads 66; and when the thermometer has dropped
degrees!

What will the the thermometer read when the temperature drops 91
degrees? If you are having problems answering this, draw a picture of
a thermometer. Make the little marks for the temperature and you will
see that the temperature will be 0 degrees if the temperature drops
91 degrees.

Well, Garry, there you are watching the thermometer drop as it gets
colder. It is now zero degrees, and you can't imagine it getting any
colder, but suddenly, it does! The temperature drops one more degree,
so that it is now 92 degrees colder outside than it was when you put
your shorts on! What will the thermometer read now? Look at a real
thermometer if you are still having problems....you will see that it
reads -1 degree. And we *know* how cold that is!

My point with this long explanation is to show you that you *do* know
how to do subtraction with negative numbers. If you draw a number
line, you will see that it is simpler than you thought:

<--(-4)----(-3)----(-2)----(-1)----0----1----2----3----4----5-->

If we were to do the subtraction problem  5-7 , we would put our
pencil on 5 and go back 7 units. What is the answer? Yes, it is -2. To
prove that our answer is correct, we could add -2 to 7 by putting our
pencil on -2 and counting up 7 units. We return to 5!

If you start getting lost, wondering whether you should go left or
right on the number line, just remember that addition INCREASES the
values of numbers so that you must go right. Subtraction DECREASES the
values of numbers, so we go left. (Please note that word processors
make drawing number lines difficult, but these numbers are an equal
distance apart!)

I hope this not only helps you answer this math problem, but also any
future subtraction problems that involve negative numbers!

-Doctor Reno,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Negative Numbers

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search