Explanation:

To solve this problem, we need to replace the given mathematical operators with their new meanings and then evaluate the expression following the order of operations (BODMAS/PEMDAS). **Step 1: List the original expression and the new operator meanings.** * Original expression: $26 \div 13 \times 8 + 6 - 2$ * New meanings: * '$\times$' means '+' (addition) * '$\div$' means '-' (subtraction) * '+' means '$\times$' (multiplication) * '-' means '$\div$' (division) **Step 2: Substitute the new operator meanings into the expression.** * The expression $26 \div 13 \times 8 + 6 - 2$ becomes: * $26 \text{ (new } \div \text{)} 13 \text{ (new } \times \text{)} 8 \text{ (new } + \text{)} 6 \text{ (new } - \text{)} 2$ * $26 - 13 + 8 \times 6 \div 2$ **Step 3: Evaluate the new expression following the order of operations (BODMAS/PEMDAS).** * **B**rackets (None) * **O**rders (Powers and Square Roots) (None) * **DM** Division and Multiplication (from left to right) * First, perform the division: $6 \div 2 = 3$ * The expression is now: $26 - 13 + 8 \times 3$ * Next, perform the multiplication: $8 \times 3 = 24$ * The expression is now: $26 - 13 + 24$ * **AS** Addition and Subtraction (from left to right) * First, perform the subtraction: $26 - 13 = 13$ * The expression is now: $13 + 24$ * Finally, perform the addition: $13 + 24 = 37$ \nTherefore, the value of the expression is 37. * **Option 1 (17):** This would be incorrect, likely from an error in applying operator precedence or substitution. For example, if multiplication was done before division, or if addition/subtraction order was incorrect. * **Option 2 (27):** This is incorrect. The calculation does not result in 27. * **Option 3 (37):** This matches our calculated value. So, this is the correct answer. * **Option 4 (47):** This is incorrect. The calculation does not result in 47.