Use the order of operations to simplify this expression \( \left(\frac{3}{5}+\frac{13}{20}\right) \cdot \frac{1}{2} \)

First, let's simplify the expression inside the parentheses, \( \frac{3}{5}+\frac{13}{20} \). To add these fractions, we need a common denominator. The least common multiple of 5 and 20 is 20. Thus, we convert \( \frac{3}{5} \) to \( \frac{12}{20} \) (by multiplying both the numerator and the denominator by 4). Now we can add: \[ \frac{12}{20} + \frac{13}{20} = \frac{25}{20} \] Now, we multiply \( \frac{25}{20} \) by \( \frac{1}{2} \): \[ \frac{25}{20} \cdot \frac{1}{2} = \frac{25 \cdot 1}{20 \cdot 2} = \frac{25}{40} \] Finally, we simplify \( \frac{25}{40} \) by dividing both the numerator and the denominator by 5: \[ \frac{25 \div 5}{40 \div 5} = \frac{5}{8} \] So, the simplified expression is \( \frac{5}{8} \).