1. **State the problem:** Simplify the expression $$9 \left(\frac{3}{14}\right) - \left(4 \left(\frac{3}{4}\right) + 2 \left(\frac{5}{7}\right)\right)$$ 2. **Rewrite mixed numbers as improper fractions:** - $$9 \left(\frac{3}{14}\right)$$ is already a multiplication of an integer and a fraction. - $$4 \left(\frac{3}{4}\right) = 4 \times \frac{3}{4}$$ - $$2 \left(\frac{5}{7}\right) = 2 \times \frac{5}{7}$$ 3. **Calculate each term:** - $$9 \times \frac{3}{14} = \frac{27}{14}$$ - $$4 \times \frac{3}{4} = \frac{12}{4} = 3$$ - $$2 \times \frac{5}{7} = \frac{10}{7}$$ 4. **Simplify inside the parentheses:** - $$4 \left(\frac{3}{4}\right) + 2 \left(\frac{5}{7}\right) = 3 + \frac{10}{7} = \frac{21}{7} + \frac{10}{7} = \frac{31}{7}$$ 5. **Subtract the terms:** - $$\frac{27}{14} - \frac{31}{7} = \frac{27}{14} - \frac{62}{14} = -\frac{35}{14} = -\frac{5}{2}$$ 6. **Final simplified result:** $$-\frac{5}{2}$$ --- 1. **State the problem:** Simplify the expression $$\frac{3 \left(\frac{2}{3}\right)}{6 - 4 \left(\frac{1}{3}\right)}$$ 2. **Calculate numerator:** - $$3 \times \frac{2}{3} = 2$$ 3. **Calculate denominator:** - $$4 \times \frac{1}{3} = \frac{4}{3}$$ - $$6 - \frac{4}{3} = \frac{18}{3} - \frac{4}{3} = \frac{14}{3}$$ 4. **Divide numerator by denominator:** - $$\frac{2}{\frac{14}{3}} = 2 \times \frac{3}{14} = \frac{6}{14} = \frac{3}{7}$$ 5. **Final simplified result:** $$\frac{3}{7}$$