Chapter 12.1, Problem 4P

a. Explain how to decompose the large rectangle in Figure 12.5 into $4\frac{1}{2}$ groups with $5\frac{3}{4}$ squares in each group, so as to describe the area of the rectangle as

 

Figure 12.4 Explain why the area is ( $4\frac{1}{2}$ . $5\frac{3}{4}$ ) $c{m}^2$

b.. Calculate $4\frac{1}{2}$ . $5\frac{3}{4}$ without a calculator, showing your calculations. Then verify that this calculation has the same answer as when you determine the area of the rectangle in Figure 12.5 by counting squares.