2. You can use a rectangle to represent \( (0.3) \cdot(0.5) \). a. What must the side length of each square represent for the rectangl correctly represent \( (0.3) \cdot(0.5) \) ? b. What area is represented by each square? c. What is \( (0.3) \cdot(0.5) \) ? Show your reasoning.

To represent \( (0.3) \cdot(0.5) \) using a rectangle, each side length of the rectangle must represent a fraction of the whole unit. Specifically, each square should be a section of a square that is \( 1 \) by \( 1 \); thus, you could divide the unit square into ten equal sections along one side (for \( 0.3 \) representing 3 out of 10) and two equal sections along the other (for \( 0.5 \) representing 5 out of 10). The area of each square represents the product of the lengths of the sides. Since \( 0.3 \) corresponds to \( \frac{3}{10} \) and \( 0.5 \) corresponds to \( \frac{5}{10} \), the area represented by each square is calculated as \( 0.3 \times 0.5 = 0.15 \). This area reflects 15 out of 100 parts of the unit square, illustrating the concept of multiplying decimals. Thus, \( (0.3) \cdot(0.5) = 0.15 \). The reasoning follows from the understanding that multiplying two decimal values creates a smaller area that showcases how products scale down in the unit square context.