what are all fractions that are equivalent to -4/9

Answer 1

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:

1. Multiply by 1: $-\frac{4\times 1}{9\times 1}=-\frac{4}{9}$
2. Multiply by 2: $-\frac{4\times 2}{9\times 2}=-\frac{8}{18}$
3. Multiply by 3: $-\frac{4\times 3}{9\times 3}=-\frac{12}{27}$
4. Multiply by -1: $-\frac{4\times -1}{9\times -1}=\frac{4}{9}$ (positive equivalent)
5. Multiply by -2: $-\frac{4\times -2}{9\times -2}=\frac{8}{18}$
6. 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 $n\ne 0$.

Thus, any fraction of the form $-\frac{4n}{9n}$ is equivalent to $-\frac{4}{9}$, where $n$ is a non-zero integer.