Fraction Multiplication Dfedb1

1. **State the problem:** Simplify the expression $$-\frac{1}{4} \times \left(-\frac{3}{5}\right) \times \left(-\frac{2}{3}\right)$$. 2. **Recall the multiplication of fractions rule:** Multiply numerators together and denominators together. 3. **Multiply the numerators:** $$-1 \times (-3) \times (-2) = -1 \times 3 \times (-2) = -3 \times (-2) = 6$$ but note the signs carefully: actually $$-1 \times (-3) = 3$$ and then $$3 \times (-2) = -6$$. 4. **Multiply the denominators:** $$4 \times 5 \times 3 = 60$$. 5. **Combine numerator and denominator:** $$\frac{-6}{60}$$. 6. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor, which is 6. 7. **Show cancellation:** $$\frac{\cancel{6} \times (-1)}{\cancel{6} \times 10} = \frac{-1}{10}$$. 8. **Final answer:** $$-\frac{1}{10}$$. Thus, the simplified value of the expression is $$-\frac{1}{10}$$.