\( 6+\frac{1}{2} \) of \( 30 \div(9-0) \) \( 3^{2}+5 \times 3-6 \div 3 \)

Let's evaluate each of the given mathematical expressions step by step. ### 1. \( 6 + \frac{1}{2} \) of \( 30 \div (9 - 0) \) **Step 1: Simplify the expression inside the parentheses** \[ 9 - 0 = 9 \] **Step 2: Perform the division** \[ 30 \div 9 = \frac{30}{9} = \frac{10}{3} \] **Step 3: Calculate \(\frac{1}{2}\) of \(\frac{10}{3}\)** \[ \frac{1}{2} \times \frac{10}{3} = \frac{10}{6} = \frac{5}{3} \] **Step 4: Add 6 to the result** \[ 6 + \frac{5}{3} = \frac{18}{3} + \frac{5}{3} = \frac{23}{3} = 7\frac{2}{3} \] **Final Result:** \[ 6 + \frac{1}{2} \text{ of } 30 \div (9 - 0) = \frac{23}{3} \text{ or } 7\frac{2}{3} \] --- ### 2. \( 3^{2} + 5 \times 3 - 6 \div 3 \) **Step 1: Calculate the exponent** \[ 3^{2} = 9 \] **Step 2: Perform the multiplication** \[ 5 \times 3 = 15 \] **Step 3: Perform the division** \[ 6 \div 3 = 2 \] **Step 4: Combine all the results** \[ 9 + 15 - 2 = 22 \] **Final Result:** \[ 3^{2} + 5 \times 3 - 6 \div 3 = 22 \]