To solve and simplify the expression \(-\frac{3}{4} \times \frac{2}{5}\), we can multiply the numerators and the denominators:
\[ -\frac{3}{4} \times \frac{2}{5} = \frac{-3 \times 2}{4 \times 5} = \frac{-6}{20} \]
Now, we can simplify \(\frac{-6}{20}\) by finding the greatest common divisor (GCD) of 6 and 20, which is 2:
\[ \frac{-6 \div 2}{20 \div 2} = \frac{-3}{10} \]
Now let's also evaluate the second expression \(-\frac{4}{3} \times \frac{5}{2}\):
Again, we multiply the numerators and the denominators:
\[ -\frac{4}{3} \times \frac{5}{2} = \frac{-4 \times 5}{3 \times 2} = \frac{-20}{6} \]
Next, we can simplify \(\frac{-20}{6}\) by dividing both the numerator and the denominator by their GCD, which is 2:
\[ \frac{-20 \div 2}{6 \div 2} = \frac{-10}{3} \]
So, the final simplified results are:
- \(-\frac{3}{4} \times \frac{2}{5} = \frac{-3}{10}\)
- \(-\frac{4}{3} \times \frac{5}{2} = \frac{-10}{3}\)