# Pre-Algebra Equation with Negative Mixed Number

• Aug 31st 2009, 06:16 PM
ZushiRoe
Pre-Algebra Equation with Negative Mixed Number
I am very unsure of how to solve this equation, which involves a negative mixed number. Help would be very much appreciated.

-6/n = -9 5/6
• Aug 31st 2009, 07:22 PM
pickslides
$\displaystyle \frac{-6}{n} = -9\frac{5}{6}$

$\displaystyle \frac{-6}{-9} = \frac{5}{6}n$

$\displaystyle \frac{5}{6}n = \frac{6}{9}$

$\displaystyle n = \frac{6\times 6}{9\times 5}$

$\displaystyle n = \frac{36}{45}$
• Aug 31st 2009, 07:54 PM
ZushiRoe
I'm sorry, but I don't exactly understand your reasoning. May you please explain?
• Aug 31st 2009, 07:58 PM
pickslides
I solved for n by isolating it.
• Aug 31st 2009, 08:02 PM
ZushiRoe
Thank you for replying. I'm still not sure how the method you used to isolate "n" with works. May you please explain this as well, if it isn't too much of a problem.
• Aug 31st 2009, 08:02 PM
Chris L T521
Quote:

Originally Posted by pickslides
$\displaystyle \frac{-6}{n} = -9\frac{5}{6}$

$\displaystyle \frac{-6}{-9} = \frac{5}{6}n$

$\displaystyle \frac{5}{6}n = \frac{6}{9}$

$\displaystyle n = \frac{6\times 6}{9\times 5}$

$\displaystyle n = \frac{36}{45}$

$\displaystyle -9\frac{5}{6}\neq -9\cdot\frac{5}{6}$. However, $\displaystyle -9\frac{5}{6}=-9-\frac{5}{6}$.

So first rewrite it as an improper fraction:

$\displaystyle \frac{-6}{n}=-\frac{59}{6}\implies \frac{6\cdot 6}{59}=n\implies\frac{36}{59}=n$
• Aug 31st 2009, 08:11 PM
pickslides
Quote:

Originally Posted by Chris L T521
$\displaystyle -9\frac{5}{6}\neq -9\cdot\frac{5}{6}$. However, $\displaystyle -9\frac{5}{6}=-9-\frac{5}{6}$.

So first rewrite it as an improper fraction:

$\displaystyle \frac{-6}{n}=-\frac{59}{6}\implies \frac{6\cdot 6}{59}=n\implies\frac{36}{59}=n$

• Aug 31st 2009, 08:57 PM
ZushiRoe
I'm sorry, but I am still very confounded by how all of this works. Why does

$\displaystyle -9-\frac{5}{6}$
make sense?

As well, why do all the digits become positive, and 59 somehow becomes the denominator of the answer? This is all so confusing.
• Aug 31st 2009, 09:27 PM
pickslides
$\displaystyle -9\frac{5}{6} = -\frac{9\times 6 + 5}{6} = \frac{-59}{6}$

$\displaystyle -9-\frac{5}{6} = \frac{-54}{6}-\frac{5}{6}= \frac{-59}{6}$

Therefore $\displaystyle -9\frac{5}{6} = -9-\frac{5}{6}$
• Sep 1st 2009, 01:54 PM
pickslides
Quote:

Originally Posted by ZushiRoe

As well, why do all the digits become positive,

If you follow my first post, being mindful of the arithmetic error pointed out by Chris L T521, you will notice a negative number being divided by another negative number, what is the result?