Chapter 3.4, Problem 10P

1. John says $\frac{2}{3}+\frac{3}{3}=\frac{4}{6}$ and uses the drawing in Figure 3.30 as evidence. Discuss what is wrong with John’s reasoning. What underlying misconception does John have? Don’t just explain how to do the problem correctly; explain why John’s reasoning is faulty.

 

   Figure 3.30 Showing how $\frac{2}{3}+\frac{3}{3}=\frac{4}{6}$ .

2. Explain how John could reas about the sizes of the numbers to see that his answer is not correct.