1. **Problem statement:** The product of two fractions is $\frac{4}{25}$. The quotient of the larger fraction divided by the smaller fraction is 4. Find the two fractions. 2. **Set variables:** Let the smaller fraction be $x$ and the larger fraction be $y$. 3. **Write equations:** - Product: $$xy = \frac{4}{25}$$ - Quotient: $$\frac{y}{x} = 4$$ 4. **Express $y$ in terms of $x$:** $$y = 4x$$ 5. **Substitute into product equation:** $$x \times 4x = \frac{4}{25}$$ $$4x^2 = \frac{4}{25}$$ 6. **Divide both sides by 4:** $$\cancel{4}x^2 = \frac{4}{25} \div \cancel{4}$$ $$x^2 = \frac{1}{25}$$ 7. **Solve for $x$:** $$x = \pm \frac{1}{5}$$ Since $x$ is a fraction and smaller, take positive value: $$x = \frac{1}{5}$$ 8. **Find $y$:** $$y = 4x = 4 \times \frac{1}{5} = \frac{4}{5}$$ 9. **Answer:** The two fractions are $\frac{1}{5}$ and $\frac{4}{5}$.