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### Reciprocals of Negative Fractions

```
Date: 03/19/2002 at 02:01:47
From: Melissa
Subject: Reciprocals

What is a reciprocal, and what is the reciprocal of negative 1/2?
What is the reciprocal of 10?
```

```
Date: 03/19/2002 at 09:06:09
From: Doctor Rick
Subject: Re: Reciprocals

Hi, Melissa.

You have learned that the reciprocal of, say, 2/3 is 3/2, right? To
get the reciprocal of a fraction, you just switch the numerator and
the denominator.

So what happens if the fraction is negative? You can consider the
negative sign to be part of the numerator: think of -1/2 as -1 over 2.
Then the reciprocal is 2/(-1). But you can make an equivalent fraction
by multiplying the numerator and denominator by the same quantity. Try
multiplying both by -1:

2     2*-1   -2
--- = ----- = ---
-1    -1*-1    1

Now, a fraction with a denominator of 1 is just a whole number, so the
reciprocal of -1/2 is -2.

This last part gives us a clue as to how to find the reciprocal of
whole numbers like 10. We can write the number with a denominator
of 1:

10 = 10/1

Then we take the reciprocal of this fraction: switch the numerator and
denominator to get 1/10.

Does this help?

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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