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This question may be very simple, but I get confused on things like it.

If I have a fraction like this:

$-\frac{x}{-2}$

How can I convert this negative fraction to a positive one? It does not matter if the numerator or denominator is negative of positive, I just need to get rid of the main one. However, I think that $-\frac{x}{-2}$ is equal to $\frac{-x}{-2}$, is this true?

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  • $\begingroup$ Give it a try with some numbers, you'll see it immediately, formally without the numbers, you can have a look at the answer below. $\endgroup$ – Bob Jan 30 '13 at 12:44
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For any real numbers $a$ and $b\neq 0$, we have $-\frac{a}{b}=\frac{-a}{b}=\frac{a}{-b}$. Also, $-\frac{-a}{b}=-\frac{a}{-b}=\frac{-a}{-b}=\frac{a}{b}$.

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  • $\begingroup$ To answer your question directly, @user60161, you can simply remove both of the negative signs to get $\frac x 2$. $\endgroup$ – Joe Z. Jan 30 '13 at 3:50
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Realize that negative signs represent multiplying the number by $-1$. Any fraction can be multiplied by $\frac aa$ without changing the value, since it equals one. So, multiply your fraction by $\frac {-1}{-1}$ to clear negative signs (or to move them between the top and bottom).

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I think that $-\frac{x}{-2}$ is equal to $\frac{-x}{-2}$, is this true?

Yes, indeed: $$-\frac{x}{-2} = -1 \times \frac{x}{-2} = \frac {-1}{1}\times \frac x{-2} = \frac{-x}{-2}$$

But you can simplify further: $$\frac{-x}{-2} = \frac{-1\times x}{-1\times 2} = \frac x2$$ by cancelling $-1$ of in the numerator and denominator.

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