Chapter 5.1, Problem 13P

a. Write a word problem for $2\frac{1}{2}.3\frac{1}{2}=?$

b. Use math drawings and the definition of multiplication to solve the problem.

c. Use the distributive property to calculate $2\frac{1}{2}.3\frac{1}{2}$ by rewriting this product as $\left(2+\frac{1}{2}\right).\left(3+\frac{1}{2}\right)$ .

d. Identify the four terms produced by the distributive property (in part [c])in a math drawing like the one in part (b).

e. Now write the mixed numbers $2\frac{1}{2}$ and $3\frac{1}{2}$ as improper fractions, and use the standard procedure for multiplying fractions to calculate $2\frac{1}{2}.3\frac{1}{2}.$ How do you see the product of the numerators in your drawing in part (b)? How can you see the product of the denominators in your drawing?