To find the fractions that are equivalent to \(-\frac{4}{9}\), we will consider each option given:
A. \(49\frac{4}{9}\) – This is a mixed number representing \(49 + \frac{4}{9}\), which is not equivalent to \(-\frac{4}{9}\).
B. \(-\frac{4}{9}\) – This is exactly the original fraction we have, so it is equivalent.
C. \(-\frac{4}{-9}\) – This simplifies to \(\frac{4}{9}\), which is also not equivalent to \(-\frac{4}{9}\).
D. \(-\left(49 + \frac{4}{9}\right)\) – This represents the negative of a positive number plus a fraction, which is not equivalent to our target.
E. \(-\frac{-4}{-9}\) – This simplifies to \(-\frac{4}{-9}\), which becomes \(\frac{4}{9}\), hence not equivalent.
F. \(-\left(-49 - \frac{4}{9}\right)\) – This changes to \(49 + \frac{4}{9}\), which is again not equivalent to \(-\frac{4}{9}\).
After reviewing all options, the only equivalent fraction to \(-\frac{4}{9}\) is:
B: \(-\frac{4}{9}\).