# Thread: Pre-Algebra Equation with Negative Mixed Number

1. ## 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

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

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

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

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

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

3. I'm sorry, but I don't exactly understand your reasoning. May you please explain?

4. I solved for n by isolating it.

5. 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.

6. 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:

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

7. 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:

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

8. 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.

9. $\displaystyle -9\frac{5}{6} = -\frac{9\times 6 + 5}{6} = \frac{-59}{6}$

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

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

10. 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?