1.Which is greater? How do you know? \[ 3 \frac{1}{2} \times \frac{1}{3} \text { or } \frac{2}{3} \times \frac{3}{2} \]

Let's break this down step-by-step! First, we convert \(3 \frac{1}{2}\) to an improper fraction, which is \(\frac{7}{2}\). Now, we can calculate the first expression: \[ 3 \frac{1}{2} \times \frac{1}{3} = \frac{7}{2} \times \frac{1}{3} = \frac{7}{6}. \] For the second expression, we simplify it: \[ \frac{2}{3} \times \frac{3}{2} = 1. \] Now we compare \(\frac{7}{6}\) (which is approximately 1.16667) to 1. Clearly, \(\frac{7}{6}\) is greater than 1. Thus, \(3 \frac{1}{2} \times \frac{1}{3}\) is greater than \(\frac{2}{3} \times \frac{3}{2}\). So, the answer is: \[ 3 \frac{1}{2} \times \frac{1}{3} \text{ is greater.} \]