To solve $\frac{12}{15} \div \frac{24}{45}$, follow these steps:

1. Rewrite the division as multiplication: $\frac{12}{15} \div \frac{24}{45} = \frac{12}{15} \times \frac{45}{24}$ In division of fractions, we multiply by the reciprocal of the second fraction.

2. Simplify each fraction if possible: $\frac{12}{15} = \frac{4}{5} \quad \text{(divide both numerator and denominator by 3)}$ $\frac{45}{24} = \frac{15}{8} \quad \text{(divide both numerator and denominator by 3)}$

3. Multiply the fractions: $\frac{4}{5} \times \frac{15}{8} = \frac{4 \times 15}{5 \times 8} = \frac{60}{40}$

4. Simplify the resulting fraction: $\frac{60}{40} = \frac{3}{2} \quad \text{(divide both numerator and denominator by 20)}$

Thus, $\frac{12}{15} \div \frac{24}{45} = \frac{3}{2}$.

Would you like more details or have any questions?

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Here are five related questions:

1. How do you divide fractions involving mixed numbers?
2. What is the reciprocal of a fraction?
3. How can you simplify complex fractions?
4. How do you convert improper fractions to mixed numbers?
5. What are the steps to multiply and divide decimals?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the divisor fraction.