Expression Symbols Defined

The problem presents a mathematical expression where specific letters represent arithmetic operations:

• 'P' stands for Addition (+)
• 'D' stands for Subtraction (-)
• 'S' stands for Multiplication (\times)
• 'V' stands for Division (\div)

The given expression is: 15 S 2 P 2 (11 S 2) D 75 V 15 D 4 (9 S 4)

First, we substitute the letters with their corresponding mathematical operators:

15 \times 2 + 2 \times (11 \times 2) - 75 \div 15 - 4 \times (9 \times 4)

Calculation Strategy: Order of Operations

To find the correct value, we must follow the standard order of operations (often remembered by acronyms like BODMAS or PEMDAS):

1. Brackets / Parentheses
2. Orders / Exponents
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Step 1: Parentheses Evaluation

We start by calculating the expressions inside the parentheses:

• (11 \times 2) = 22
• (9 \times 4) = 36

Substituting these results back into the expression:

15 \times 2 + 2 \times 22 - 75 \div 15 - 4 \times 36

Step 2: Multiplication and Division

Next, we perform all multiplication and division operations from left to right:

• 15 \times 2 = 30
• 2 \times 22 = 44
• 75 \div 15 = 5
• 4 \times 36 = 144

Now, the expression becomes:

30 + 44 - 5 - 144

Step 3: Addition and Subtraction

Finally, we perform addition and subtraction operations from left to right:

• 30 + 44 = 74
• 74 - 5 = 69
• 69 - 144 = -75

Final Result

Therefore, the value of the given expression after decoding the symbols and applying the order of operations is -75.