1. **State the problem:** We need to calculate $45$ divided by $\frac{2}{5}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $a \div \frac{b}{c} = a \times \frac{c}{b}$. 3. **Apply the rule:** $$45 \div \frac{2}{5} = 45 \times \frac{5}{2}$$ 4. **Multiply:** $$45 \times \frac{5}{2} = \frac{45 \times 5}{2} = \frac{225}{2}$$ 5. **Simplify or convert to decimal:** $$\frac{225}{2} = 112.5$$ 6. **Final answer:** $$45 \div \frac{2}{5} = 112.5$$