Reason Inductively Find two rational numbers greater than \( \frac{1}{4} \) whose product is less than \( \frac{1}{4} \). Explain.

One example of two rational numbers that meet the criteria is \( \frac{1}{2} \) and \( \frac{1}{3} \). Both of these numbers are greater than \( \frac{1}{4} \), and when multiplied together, their product is: \[ \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \] Now, \( \frac{1}{6} \) is indeed less than \( \frac{1}{4} \), satisfying the requirement. Another pair could be \( \frac{3}{8} \) and \( \frac{5}{8} \). Both are greater than \( \frac{1}{4} \) as well, and their product is: \[ \frac{3}{8} \times \frac{5}{8} = \frac{15}{64} \] Since \( \frac{15}{64} \) is approximately \( 0.234375 \), which is also less than \( \frac{1}{4} \) (or \( 0.25 \)), they fit the bill perfectly!