### Numbers: Fractions

### Negative fractions

Negative fractions

The rules for fractions containing negative numbers are comparable to the rules for dividing negative numbers:

\[\begin{array}{rclrcl}

\dfrac{\green{\text{positive}}}{\green{\text{positive}}} &=&\green{\text{positive}}\\[5pt]

\dfrac{\green{\text{positive}}}{\blue{\text{negative}}} &=&\blue{\text{negative}}\\[5pt]

\dfrac{\blue{\text{negative}}}{\green{\text{positive}}} &=& \blue{ \text{negative}} \\[5pt]

\dfrac{\blue{\text{negative}}}{\blue{\text{negative}}} &=&\green{\text{positive}} \\

\end{array}\]

**Examples**

\[\begin{array}{rcl|rcl}\require{color}

\\\phantom{xxx}\\

\dfrac{\green2}{\green3} &=& \green{\dfrac{2}{3}} \\[10pt]

\dfrac{\green2}{\blue{-3}} &=&\blue{-\dfrac{2}{3}}\\[10pt]

\dfrac{\blue{-2}}{\green3} &=&\blue{-\dfrac{2}{3}}\\[10pt]

\dfrac{\blue{-2}}{\blue{-3}} &=& \green{\dfrac{2}{3}} \\

\end{array}\]

The fraction #\dfrac{-5}{-11}# is positive because two negative numbers divided by each other give a positive number. The other fractions should, therefore, also be positive. That means the number of minus signs in each fraction should be even. This gives:

\[\dfrac{-5}{-11}=\dfrac{5}{11}=-\dfrac{5}{-11}\]

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