Refer to your work from problems 11-21 and 11-26.

1. In problem 11-21, you found the sums of three pairs of rational numbers. Was each sum a rational number? Justify your answer.

   Answer (a):

   Yes, each sum was a fraction and therefore a rational number.

2. Will that always be true? In other words, is the set of rational numbers closed under addition? Justify your answer. Hint: What is $\frac { a } { b } + \frac { c } { d }$?

   Hint (b):

   $\text{Is your answer to }\frac{a}{b}+\frac{c}{d} \text{ another rational number?}$