On the Back! 8. Find the product of \( \frac{5}{7} \times \frac{2}{5} \). Use an area model to help solve.

To find the product of \( \frac{5}{7} \times \frac{2}{5} \) using an area model, visualize a rectangle divided into sections that represent the fractions. First, draw a rectangle and divide it into 7 equal vertical parts to represent \( \frac{5}{7} \). Shade 5 of those sections. Then, divide the same rectangle horizontally into 5 equal sections to represent \( \frac{2}{5} \). Shade 2 of those sections. The overlapping shaded area will represent the product of the two fractions, which amounts to \( \frac{10}{35} \) after combining the areas. Simplifying this gives you \( \frac{2}{7} \). Now, to make things clearer and avoid confusion: when multiplying fractions, it's easy! Just multiply the numerators (top numbers) together and the denominators (bottom numbers) together. In this case, \( 5 \times 2 = 10 \) for the numerator and \( 7 \times 5 = 35 \) for the denominator. Simplify \( \frac{10}{35} \) to get \( \frac{2}{7} \)! So remember, it's all about multiplying straight across, and when in doubt, an area model makes it visually simple!