Question

4 select all fractions that are equivalent to $\frac{-4}{9}$
a $-\frac{-4}{9}$
b $\frac{4}{-9}$
c $-\frac{4}{-9}$
d $\frac{-4}{-9}$
e $\frac{4}{9}$
f $-(\frac{4}{9})$

Explanation:

Step1: Analyze sign rules for fractions

A negative fraction can be written as $\frac{-a}{b}$, $\frac{a}{-b}$, or $-\frac{a}{b}$, since $\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}$.

Step2: Evaluate each option

• Option A: $-\frac{4}{9}$ matches $-\frac{a}{b}$ form, so equivalent to $\frac{-4}{9}$.
• Option B: $\frac{4}{-9}$ matches $\frac{a}{-b}$ form, so equivalent to $\frac{-4}{9}$.
• Option C: $-\frac{4}{-9} = \frac{4}{9}$, which is positive, not equivalent.
• Option D: $\frac{-4}{-9} = \frac{4}{9}$, which is positive, not equivalent.
• Option E: $\frac{4}{9}$ is positive, not equivalent.
• Option F: $-(\frac{4}{9}) = -\frac{4}{9}$, matches $-\frac{a}{b}$ form, so equivalent to $\frac{-4}{9}$.

Answer:

A. $-\frac{4}{9}$, B. $\frac{4}{-9}$, F. $-(\frac{4}{9})$