1. **State the problem:** Simplify the expression $$\frac{\frac{1}{8} + \frac{3}{40}}{\frac{1}{8}}$$ and compare it to the fraction $$\frac{9}{5}$$. 2. **Find a common denominator for the numerator:** The fractions in the numerator are $$\frac{1}{8}$$ and $$\frac{3}{40}$$. The least common denominator is 40. 3. **Convert fractions:** $$\frac{1}{8} = \frac{5}{40}$$ 4. **Add the fractions in the numerator:** $$\frac{5}{40} + \frac{3}{40} = \frac{5+3}{40} = \frac{8}{40}$$ 5. **Simplify the numerator:** $$\frac{8}{40} = \frac{\cancel{8}}{\cancel{40}} = \frac{1}{5}$$ 6. **Rewrite the original expression:** $$\frac{\frac{1}{5}}{\frac{1}{8}}$$ 7. **Divide the fractions by multiplying by the reciprocal:** $$\frac{1}{5} \times \frac{8}{1} = \frac{8}{5}$$ 8. **Compare the result to $$\frac{9}{5}$$:** $$\frac{8}{5} \neq \frac{9}{5}$$ **Final answer:** The simplified value of the expression is $$\frac{8}{5}$$, which is not equal to $$\frac{9}{5}$$.