Chapter 6.4, Problem 6P

Jose and Mark are making cookies for a bake sale. Their recipe calls for $2\frac{1}{4}$ cups of flour for each batch. They have 5 cups of flour. Jose and Mark realize that they can make two batches of cookies and that there will be some flour left. Since the recipe doesn't call for eggs, and since they have plenty of the other ingredients on hand, they decide they can make a fraction of a batch in addition to the two whole batches. But Jose and Mark have a difference of opinion. Jose says that $5÷2\frac{1}{4}=2\frac{2}{9}$ so he says that they can make $2\frac{2}{9}$ batches of cookies. Mark says that two batches of cookies will use up $4\frac{1}{2}$ cups of flour, leaving $\frac{1}{2}$ left, so they should be able to make $2\frac{1}{2}$ batches. Mark draws the picture in Figure 6.20 to explain his thinking to Jose.

Figure 6.20 Representing $5÷2\frac{1}{4}$ by considering how many $2\frac{1}{4}$ cups of flour are in 5 cups of flour.

Discuss the boys' mathematics: What's right, what's not right, and why? If anything is incorrect, how could you modify it to make it correct?