Question

Select ALL fractions that are equivalent to -4/9.

Answer 1

To find fractions that are equivalent to \(-\frac{4}{9}\), you can multiply both the numerator and the denominator of the fraction by the same non-zero integer. Here are a few examples:

1. Multiply by \(2\):
\[
-\frac{4 \times 2}{9 \times 2} = -\frac{8}{18}
\]

2. Multiply by \(3\):
\[
-\frac{4 \times 3}{9 \times 3} = -\frac{12}{27}
\]

3. Multiply by \(-1\):
\[
-\frac{4 \times -1}{9 \times -1} = \frac{4}{9}
\]
This is not equivalent as it's the positive version.

4. Multiply by \(-2\):
\[
-\frac{4 \times -2}{9 \times -2} = \frac{8}{18}
\]

The general form of an equivalent fraction to \(-\frac{4}{9}\) is:
\[
-\frac{4k}{9k}
\]
where \(k\) is any non-zero integer.

Thus, some examples of equivalent fractions to \(-\frac{4}{9}\) include:
- \(-\frac{8}{18}\)
- \(-\frac{12}{27}\)
- etc.

Any fraction in the form \(-\frac{4k}{9k}\) with non-zero \(k\) will be equivalent to \(-\frac{4}{9}\).