Hi all;

So why avoid negative denominators?

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- May 5th 2011, 02:41 AManthonyeavoid negative denominators
Hi all;

So why avoid negative denominators? - May 5th 2011, 02:44 AMUnknown008
- May 5th 2011, 02:49 AManthonye
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 AMUnknown008
Hm... I'mstill unsure, but I think you mean that:

$\displaystyle \frac{1}{-2}$

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