1. Let's start by stating the problem: we want to understand how to divide fractions and rewrite the entire expression accordingly. 2. The general rule for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ which means we multiply the first fraction by the reciprocal of the second. 3. For example, if we have $$\frac{2}{3} \div \frac{4}{5}$$, we rewrite it as $$\frac{2}{3} \times \frac{5}{4}$$. 4. Now, multiply the numerators and denominators: $$\frac{2 \times 5}{3 \times 4} = \frac{10}{12}$$. 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (2): $$\frac{\cancel{10}^{5}}{\cancel{12}^{6}} = \frac{5}{6}$$. 6. So, $$\frac{2}{3} \div \frac{4}{5} = \frac{5}{6}$$. 7. In summary, to divide fractions, flip the second fraction and multiply, then simplify the result if possible.