Algebraic Fractions Ba7285

1. Let's start with an example of multiplication of algebraic fractions. Given: $$\frac{2x}{3} \times \frac{4}{5x}$$ 2. The formula for multiplying fractions is: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. Applying the formula: $$\frac{2x}{3} \times \frac{4}{5x} = \frac{2x \times 4}{3 \times 5x} = \frac{8x}{15x}$$ 4. Now simplify the fraction by canceling the common factor $x$: $$\frac{8\cancel{x}}{15\cancel{x}} = \frac{8}{15}$$ 5. So, the product is: $$\frac{8}{15}$$ --- 6. Now, let's do an example of division of algebraic fractions. Given: $$\frac{3x}{4} \div \frac{6}{8x}$$ 7. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 8. Applying the formula: $$\frac{3x}{4} \div \frac{6}{8x} = \frac{3x}{4} \times \frac{8x}{6} = \frac{3x \times 8x}{4 \times 6} = \frac{24x^2}{24}$$ 9. Simplify the fraction by canceling the common factor $24$: $$\frac{\cancel{24}x^2}{\cancel{24}} = x^2$$ 10. So, the quotient is: $$x^2$$