1. **State the problem:** Simplify the expression $$\left(\frac{3}{5} - \frac{2}{5} + \frac{1}{4}\right) \div \frac{1}{6}$$ and then evaluate $$\frac{1}{5} + \frac{1}{4}$$, $$\frac{9}{20} \div \frac{1}{6}$$, and $$\frac{20}{9} \times \frac{6}{1}$$. 2. **Simplify inside the parentheses:** $$\frac{3}{5} - \frac{2}{5} = \frac{3-2}{5} = \frac{1}{5}$$ 3. **Add $$\frac{1}{5}$$ and $$\frac{1}{4}$$:** Find common denominator 20: $$\frac{1}{5} = \frac{4}{20}, \quad \frac{1}{4} = \frac{5}{20}$$ $$\frac{4}{20} + \frac{5}{20} = \frac{9}{20}$$ 4. **Divide by $$\frac{1}{6}$$:** Dividing by a fraction is multiplying by its reciprocal: $$\frac{9}{20} \div \frac{1}{6} = \frac{9}{20} \times \frac{6}{1}$$ 5. **Multiply fractions:** $$\frac{9}{20} \times \frac{6}{1} = \frac{9 \times 6}{20 \times 1} = \frac{54}{20}$$ 6. **Simplify $$\frac{54}{20}$$:** Divide numerator and denominator by 2: $$\frac{\cancel{54}^{27}}{\cancel{20}^{10}} = \frac{27}{10}$$ 7. **Evaluate $$\frac{1}{5} + \frac{1}{4}$$ separately:** As in step 3, the sum is $$\frac{9}{20}$$. 8. **Evaluate $$\frac{9}{20} \div \frac{1}{6}$$ separately:** As in step 4, this equals $$\frac{27}{10}$$. 9. **Evaluate $$\frac{20}{9} \times \frac{6}{1}$$ separately:** Multiply numerators and denominators: $$\frac{20 \times 6}{9 \times 1} = \frac{120}{9}$$ Simplify by dividing numerator and denominator by 3: $$\frac{\cancel{120}^{40}}{\cancel{9}^{3}} = \frac{40}{3}$$ **Final answers:** - $$\left(\frac{3}{5} - \frac{2}{5} + \frac{1}{4}\right) \div \frac{1}{6} = \frac{27}{10}$$ - $$\frac{1}{5} + \frac{1}{4} = \frac{9}{20}$$ - $$\frac{9}{20} \div \frac{1}{6} = \frac{27}{10}$$ - $$\frac{20}{9} \times \frac{6}{1} = \frac{40}{3}$$