Answer
$-48$
Work Step by Step
Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$
$=32\displaystyle \div\left(-\frac{2}{3} \right)$
Dividing two numbers with different signs:
Divide their absolute values; the sign of the result is $"-"$.
Also, write $32$ as $\displaystyle \frac{32}{1}.$
$=-\left(\displaystyle \frac{32}{1} \div \frac{2}{3} \right)$
Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$.
$=-\left(\displaystyle \frac{32}{1} \cdot \frac{3}{2} \right)$
Multiply fractions:
Reduce by the common factor, 2.
$=-\left(\displaystyle \frac{16}{1} \cdot \frac{3}{1} \right)$
Now, multiply the numerators and place the product over the product of the denominators.
$=-\displaystyle \frac{48}{1}$
$=-48$
