To add the fractions \(-\frac{2}{4}\) and \(\frac{3}{9}\), we first need to find a common denominator.
- Simplify \(-\frac{2}{4}\) to \(-\frac{1}{2}\) (dividing both the numerator and the denominator by 2).
- The denominators are \(2\) and \(9\). The least common multiple (LCM) of \(2\) and \(9\) is \(18\).
Next, we convert both fractions to have this common denominator:
-
For \(-\frac{1}{2}\):
\[ -\frac{1}{2} = -\frac{1 \times 9}{2 \times 9} = -\frac{9}{18} \] -
For \(\frac{3}{9}\):
\[ \frac{3}{9} = \frac{3 \times 2}{9 \times 2} = \frac{6}{18} \]
Now we can add the two fractions: \[ -\frac{9}{18} + \frac{6}{18} = \frac{-9 + 6}{18} = \frac{-3}{18} \]
Finally, we can simplify \(\frac{-3}{18}\): \[ \frac{-3}{18} = \frac{-1}{6} \]
Thus, the result of adding \(-\frac{2}{4}\) and \(\frac{3}{9}\) is: \[ \boxed{-\frac{1}{6}} \]