# Thread: Dividing by negative fractions

1. ## Dividing by negative fractions

-1/6x = -9/10

Do I divide the -1/6 by its reciprocal?

leaving me with: X = -9/10 divided by -1/6

And I am stuck!! Please show me how it is done.

2. Originally Posted by OneidaFL
-1/6x = -9/10
Is this

$\displaystyle \displaystyle-\frac{1}{6}x=-\frac{9}{10}$

or

$\displaystyle \displaystyle-\frac{1}{6x}=-\frac{9}{10}$

?

3. Originally Posted by undefined
Is this

$\displaystyle \displaystyle-\frac{1}{6}x=-\frac{9}{10}$

or

$\displaystyle \displaystyle-\frac{1}{6x}=-\frac{9}{10}$

?
The first one is the correct one

4. Originally Posted by OneidaFL
The first one is the correct one
So yes, divide each side by -1/6, or equivalently, multiply each side by -6.

5. And I am stuck!! Please show me how it is done.

-9/10 divided by -1/6

-9.10 multiplied by -6/1?

6. The negative is no issue here.
as you usually do in any equation of the form $\displaystyle ax=b$: $\displaystyle x=\frac{b}{a}$. In your case, you have $\displaystyle x=\frac{\frac{-9}{10}}{\frac{-1}{6}}=\frac{-9}{10} \times \frac{6}{-1} = \frac{54}{10}=\frac{27}{5}$

7. Best answer with an explanation. Thanks!