1. **State the problem:** We need to find the missing number in the equation $$8 \div x = \frac{14}{5}$$ where $x$ is the missing number. 2. **Recall the division rule:** Dividing by a number is the same as multiplying by its reciprocal. So, $$8 \div x = 8 \times \frac{1}{x}$$. 3. **Rewrite the equation:** $$8 \times \frac{1}{x} = \frac{14}{5}$$. 4. **Isolate $x$:** Multiply both sides by $x$ to get rid of the denominator on the left: $$8 = \frac{14}{5} \times x$$. 5. **Solve for $x$:** Divide both sides by $\frac{14}{5}$: $$x = \frac{8}{\frac{14}{5}} = 8 \times \frac{5}{14}$$. 6. **Simplify:** $$x = \frac{8 \times 5}{14} = \frac{40}{14} = \frac{20}{7}$$. 7. **Final answer:** The missing number is $$\boxed{\frac{20}{7}}$$. This means dividing 8 by $\frac{20}{7}$ gives $\frac{14}{5}$, confirming the solution.