Answer
$ \displaystyle \frac{2}{9}$
Work Step by Step
$\displaystyle \left(\frac{-4}{9} \right)\div\left(-2 \right)=$
Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$
$\displaystyle \left(-\frac{4}{9} \right)\div\left(-2 \right)=$
Dividing two numbers with like signs:
Divide their absolute values; the sign of the result is $"+"$.
Also, write $2$ as $\displaystyle \frac{2}{1}.$
$=+\displaystyle \left(\frac{4}{9} \div \frac{2}{1} \right)$
Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$.
$=\displaystyle \frac{4}{9} \cdot \frac{1}{2} $
Multiply fractions:
Reduce by the common factor, 2.
$=\displaystyle \frac{2}{9} \cdot \frac{1}{1} $
Now, multiply the numerators and place the product over the product of the denominators.
$=\displaystyle \frac{2}{9}$
