1. **State the problem:** We are given two expressions: $$a = \frac{8}{\frac{3}{5}}$$ $$b = \frac{32}{\frac{9}{30}}$$ We need to simplify both expressions. 2. **Recall the rule for dividing by a fraction:** Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{x}{\frac{y}{z}} = x \times \frac{z}{y}$$ 3. **Simplify expression $a$:** $$a = \frac{8}{\frac{3}{5}} = 8 \times \frac{5}{3} = \frac{8 \times 5}{3} = \frac{40}{3}$$ 4. **Simplify expression $b$:** $$b = \frac{32}{\frac{9}{30}} = 32 \times \frac{30}{9} = \frac{32 \times 30}{9}$$ 5. **Simplify the fraction for $b$ by canceling common factors:** $$\frac{32 \times 30}{9} = \frac{32 \times \cancel{30}}{\cancel{9}} \times \frac{\cancel{30}}{\cancel{9}}$$ Since $9 = 3 \times 3$ and $30 = 3 \times 10$, cancel one 3: $$= 32 \times \frac{10}{3} = \frac{320}{3}$$ **Final answers:** $$a = \frac{40}{3}$$ $$b = \frac{320}{3}$$