Fractions that are equivalent to \(-\frac{4}{9}\) can be found by multiplying both the numerator and the denominator by the same non-zero integer. Here are some examples:
- Multiply by 1: \(-\frac{4 \times 1}{9 \times 1} = -\frac{4}{9}\)
- Multiply by 2: \(-\frac{4 \times 2}{9 \times 2} = -\frac{8}{18}\)
- Multiply by 3: \(-\frac{4 \times 3}{9 \times 3} = -\frac{12}{27}\)
- Multiply by -1: \(-\frac{4 \times -1}{9 \times -1} = \frac{4}{9}\) (positive equivalent)
- Multiply by -2: \(-\frac{4 \times -2}{9 \times -2} = \frac{8}{18}\)
- Multiply by -3: \(-\frac{4 \times -3}{9 \times -3} = \frac{12}{27}\)
You can continue this way with any integer \(n\):
\[ -\frac{4n}{9n} \]
for any integer \(n \neq 0\).
Thus, any fraction of the form \(-\frac{4n}{9n}\) is equivalent to \(-\frac{4}{9}\), where \(n\) is a non-zero integer.