Chapter 2.2, Problem 10P

Cake problem: Figure 2.26 represents two cakes of different sizes. Each cake was divided into 12 equal pieces. Marla ate one piece from each cake. What fraction of the total amount of cake (in the two cakes combined) did Marla eat?

  

  Figure 2.26 Two cakes, each divided into 12 equal pieces

1. Ben says: “Marla ate $\frac{2}{24}$of the cake because she ate 2 pieces out of a total of 24 pieces. .” Discuss Ben’s reasoning. Is it correct? Explain why or why not. If the two cakes were the same size instead of different sizes, would Ben’s reasoning be correct in that case? Explain.
2. Seyong says: “Marla ate 2 pieces, each of which was $\frac{1}{12}$ of cake, so according to the definition of fraction, Marla ate $\frac{2}{12}$ of the cake.” Discuss Seyong’s reasoning. Is it correct? Explain why or why not. What if the two cakes each weighed 1 pound? In that case, could Seyong’s reasoning be used to make a correct statement? Explain.
3. Explain how to solve the cake problem with valid reasoning that uses our definition of fraction.