32/75 : (-48/25)

Let's solve the expression: $$\frac{32}{75} : \left(-\frac{48}{25}\right)$$ To divide by a fraction, we multiply by its reciprocal. So we have: $$\frac{32}{75} \times \left(-\frac{25}{48}\right)$$ Now, we can simplify before multiplying: $$\frac{32}{75} \times \left(-\frac{25}{48}\right) = \frac{32 \div 16}{75 \div 25} \times \left(-\frac{25 \div 25}{48 \div 16}\right) = \frac{2}{3} \times \left(-\frac{1}{3}\right)$$ Multiplying the simplified fractions: $$\frac{2}{3} \times \left(-\frac{1}{3}\right) = -\frac{2 \times 1}{3 \times 3} = -\frac{2}{9}$$ Answer: -2/9