More Which of the following properties could be used to rewrite the expression \( \left(\frac{2}{3}, \frac{1}{5}\right), \frac{5}{2} \) as \( \frac{2}{3},\left(\frac{5}{2}, \frac{1}{5}\right) \) ? Select one: 8. The commutative property used twice

We start with the expression \[ \left(\frac{2}{3} \times \frac{1}{5}\right) \times \frac{5}{2}. \] Our goal is to rewrite it as \[ \frac{2}{3} \times \left(\frac{5}{2} \times \frac{1}{5}\right). \] Notice that the original expression groups \(\frac{2}{3}\) and \(\frac{1}{5}\) together, while the new expression groups \(\frac{5}{2}\) and \(\frac{1}{5}\). We can achieve this change by rearranging the factors. Step 1. Write the product without parentheses (since multiplication is associative): \[ \frac{2}{3} \times \frac{1}{5} \times \frac{5}{2}. \] Step 2. Use the commutative property of multiplication to swap the order of \(\frac{1}{5}\) and \(\frac{5}{2}\): \[ \frac{2}{3} \times \frac{5}{2} \times \frac{1}{5}. \] Step 3. Regroup the factors (using associativity) so that \(\frac{2}{3}\) is separate: \[ \frac{2}{3} \times \left(\frac{5}{2} \times \frac{1}{5}\right). \] In this process we have used the commutative property twice (to rearrange the order) in order to have the desired grouping. Therefore, the property used is: 8. The commutative property used twice.