# avoid negative denominators

• May 5th 2011, 02:41 AM
anthonye
avoid negative denominators
Hi all;
So why avoid negative denominators?
• May 5th 2011, 02:44 AM
Unknown008
Quote:

Originally Posted by anthonye
Hi all;
So why avoid negative denominators?

What do you mean? In what context? Can you post a question that you got where you have to avoid negative denominators?
• May 5th 2011, 02:49 AM
anthonye
I'm just looking at some fractions and it says try to avoid negative denominators.
Also it says if you follow convention you will never have negative denominators.
• May 5th 2011, 03:04 AM
Unknown008
Hm... I'mstill unsure, but I think you mean that:

$\frac{1}{-2}$

should be avoided. Well, I think that if you follow the convention, you'll write $-\frac12$ instead.

It's just a convention and there isn't a 'rule' that specifically says not to put the denominator as negative.
• May 5th 2011, 05:18 AM
Soroban
Hello, anthonye!

Quote:

So why avoid negative denominators?

I considered this question early in my teaching career.
I found two reasons why negative denominators are undesirable.
. . Forgive me for resorting to baby-talk.

(1) Naming the fraction

http://latex.codecogs.com/png.latex?...}\:\frac{3}{4}

We want a specific share of some pie.

The denominator indicates the size of the slices.
. . We have divided the pie into 4 equal parts.
. . Each part is called a "fourth".

The numerator indicates the number of slices we want.
. . We want 3 of those parts.
. . Hence, we want three fourths.

http://latex.codecogs.com/png.latex?...ree-fourths".}

http://latex.codecogs.com/png.latex?...{3}{\text{-4}}

It says "Cut the pie into -4 equal parts, and take 3 slices."
And we find that we can't do that.

We can cut a pie into two equal parts.
We can even cut a pie into one equal part (although it sounds silly).
We don't know how to cut a pie into zero equal parts.
And we certainly don't know how to cut a pie into negative-four equal parts.

[2] Common denominator?

http://latex.codecogs.com/png.latex?...{3}{\text{-}4}

The LCD seems to be -12.

http://latex.codecogs.com/png.latex?...;\frac{11}{12}

This takes more work and includes some added risk.

. . http://latex.codecogs.com/png.latex?... - \frac{3}{4}

FYI
http://latex.codecogs.com/png.latex?... \end{Bmatrix}

We may change any two of the signs.

. . http://latex.codecogs.com/png.latex?...-\frac{+3}{-4}