1. **Problem:** Identify and correct the mistake(s) in the evaluation of the expression: $$\left(-\frac{1}{6}\right) - \frac{3}{2} \times \frac{2}{5} \div \left(\frac{3}{10}\right)$$ 2. **Order of operations reminder:** - Perform multiplication and division from left to right before addition and subtraction. - Division by a fraction is the same as multiplication by its reciprocal. 3. **Step-by-step correction:** - Original expression: $$\left(-\frac{1}{6}\right) - \frac{3}{2} \times \frac{2}{5} \div \left(\frac{3}{10}\right)$$ - First, handle the division: $$\frac{2}{5} \div \frac{3}{10} = \frac{2}{5} \times \frac{10}{3} = \frac{20}{15} = \frac{4}{3}$$ - Now the expression is: $$\left(-\frac{1}{6}\right) - \frac{3}{2} \times \frac{4}{3}$$ - Multiply: $$\frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2$$ - So the expression becomes: $$\left(-\frac{1}{6}\right) - 2 = -\frac{1}{6} - 2$$ - Convert 2 to fraction with denominator 6: $$2 = \frac{12}{6}$$ - Subtract: $$-\frac{1}{6} - \frac{12}{6} = -\frac{13}{6}$$ 4. **Final answer:** $$-\frac{13}{6}$$ **Explanation:** The mistake was in incorrectly handling the division and multiplication order and incorrect simplifications. Correctly applying order of operations and fraction arithmetic leads to the final answer of $-\frac{13}{6}$.