In a coded arithmetic expression, the letters represent operations as follows: P denotes division (÷), Q denotes multiplication (x), R denotes addition (+) and S denotes subtraction (-). Using this code, what is the value of 18Q12P4R5S6?

Introduction / Context:
This question presents an arithmetic expression where each letter stands for a basic operation. P, Q, R and S are used in place of division, multiplication, addition and subtraction. To find the value of the coded expression 18Q12P4R5S6, we must translate it into a normal numerical expression and then evaluate it using standard precedence rules. This tests careful symbol decoding and accurate arithmetic.

Given Data / Assumptions:

• P denotes division (÷).
• Q denotes multiplication (x).
• R denotes addition (+).
• S denotes subtraction (-).
• Expression to evaluate: 18Q12P4R5S6.
• Standard arithmetic precedence applies after substitution.

Concept / Approach:
The problem is solved in two main stages. First, we replace P, Q, R and S with their corresponding standard operators to obtain an ordinary arithmetic expression. Second, we evaluate this expression by performing multiplication and division first, from left to right, and then performing addition and subtraction. Failure to respect the correct order of operations will give a wrong result even if the substitution is done correctly.

Step-by-Step Solution:
Step 1: Start from the coded expression: 18Q12P4R5S6. Step 2: Substitute operators: Q → ×, P → ÷, R → +, S → -. Step 3: The translated expression is 18 × 12 ÷ 4 + 5 - 6. Step 4: Apply precedence. First compute 18 × 12 = 216. Step 5: Next compute 216 ÷ 4 = 54. Step 6: Substitute these results back to get 54 + 5 - 6. Step 7: Now perform addition and subtraction from left to right: 54 + 5 = 59. Step 8: Then 59 - 6 = 53. Step 9: Therefore, the value of 18Q12P4R5S6 is 53.

Verification / Alternative check:
Rewriting the expression with brackets for emphasis, (18 × 12 ÷ 4) + 5 - 6 shows clearly that 18 and 12 are multiplied, the result is divided by 4, and only then are 5 and 6 combined. Re-evaluating 18 × 12 = 216 and 216 ÷ 4 = 54, and then performing the remaining operations confirms that 53 is the final result. No other interpretation of the operator mapping is consistent with the definitions provided, so the answer is robust.

Why Other Options Are Wrong:
Options 64, 81 and 24 typically arise from common miscalculations, such as treating 12 ÷ 4 as 3 and then multiplying 18 by 3 incorrectly, or ignoring the order of operations. Option 72 might occur if someone multiplies 18 and 4 instead of dividing 216 by 4. Since the correct computation following proper substitution and precedence gives 53, all other options are incorrect.

Common Pitfalls:
Frequent mistakes include mixing up which letter stands for which operation, for example treating P as multiplication rather than division, or Q as addition instead of multiplication. Another pitfall is to perform all operations sequentially from left to right without first carrying out the multiplication and division. To avoid these errors, always write the fully translated expression, underline the multiplication and division steps, and only then evaluate step by step.

Final Answer:
After decoding the operators and applying correct arithmetic, the value of 18Q12P4R5S6 is 53.