Fraction Operations 02E535

1. **Stating the problem:** We want to understand how to multiply and divide fractions. 2. **Multiplication of fractions formula:** To multiply two fractions $$\frac{a}{b}$$ and $$\frac{c}{d}$$, use the formula: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Important rule:** Multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. 4. **Example of multiplication:** Multiply $$\frac{2}{3}$$ by $$\frac{4}{5}$$: $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ 5. **Division of fractions formula:** To divide $$\frac{a}{b}$$ by $$\frac{c}{d}$$, multiply the first fraction by the reciprocal of the second: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ 6. **Important rule:** Dividing by a fraction is the same as multiplying by its reciprocal. 7. **Example of division:** Divide $$\frac{3}{4}$$ by $$\frac{2}{7}$$: $$\frac{3}{4} \div \frac{2}{7} = \frac{3}{4} \times \frac{7}{2} = \frac{3 \times 7}{4 \times 2} = \frac{21}{8}$$ 8. **Simplifying fractions:** If possible, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). This completes the explanation of multiplication and division of fractions with examples.