1. ## avoid negative denominators

Hi all;
So why avoid negative denominators?

2. 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?

3. 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.

4. 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.

5. Hello, anthonye!

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

$\text{Example: }\:\frac{3}{4}$

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.

$\text{Hence, }\frac{3}{4}\text{ is read "three-fourths".}$

$\text{Example: }\:\frac{3}{\text{-4}}$

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?

$\text{Example: }\:\frac{5}{3} + \frac{3}{\text{-}4}$

The LCD seems to be -12.

$\text{We have: }\:\left(\frac{\text{-}4}{\text{-}4}\right)\left(\frac{5}{3}\right) + \left(\frac{3}{3}\right)\left(\frac{3}{\text{-}4}\right) \;=\;\frac{\text{-}20}{\text{-}12} + \frac{9}{\text{-}12} \;=\; \frac{\text{-}11}{\text{-}12} \;=\;\frac{11}{12}$

This takes more work and includes some added risk.

. . $\text{I would prefer to face: }\:\frac{5}{3} - \frac{3}{4}$

FYI
$\text{A fraction has }three\text{ signs: }\:+\frac{+3}{+4} \quad\begin{Bmatrix}\text{sign of the numerator} \\ \text{sign of the denominator} \\ \text{sign of the fraction} \end{Bmatrix}$

We may change any two of the signs.

. . $+\frac{+3}{+4} \;=\;+\frac{-3}{-4} \;=\;-\frac{-3}{+4} \;=\;-\frac{+3}{-4}$