Question: 45. 10 1/4 \div 2/5
1. **State the problem:** Calculate $$10 \frac{1}{4} \div \frac{2}{5}$$.
2. **Convert mixed number to improper fraction:**
$$10 \frac{1}{4} = \frac{10 \times 4 + 1}{4} = \frac{40 + 1}{4} = \frac{41}{4}$$.
3. **Division of fractions rule:**
Dividing by a fraction is the same as multiplying by its reciprocal:
$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$.
4. **Apply the rule:**
$$\frac{41}{4} \div \frac{2}{5} = \frac{41}{4} \times \frac{5}{2}$$.
5. **Multiply numerators and denominators:**
$$\frac{41 \times 5}{4 \times 2} = \frac{205}{8}$$.
6. **Simplify if possible:**
No common factors to cancel, but we can convert to a mixed number:
$$\frac{205}{8} = 25 \frac{5}{8}$$ because $$8 \times 25 = 200$$ and remainder $$5$$.
**Final answer:** $$25 \frac{5}{8}$$.