If P denotes division, Q denotes multiplication, R denotes addition and S denotes subtraction, then what is the numerical value of the expression 18 Q 12 P 4 R 5 S 6 according to the usual rules of operator precedence?

Introduction:
This problem belongs to the category of coded mathematical operations in verbal reasoning. Instead of the usual symbols for addition, subtraction, multiplication, and division, we are given letters P, Q, R, and S, each representing a different operation. Our task is to decode the expression correctly and then evaluate it using the standard order of operations (also called BODMAS or PEMDAS rules).

Given Data / Assumptions:
The statement tells us that P denotes division, Q denotes multiplication, R denotes addition, and S denotes subtraction. The coded expression to be evaluated is 18 Q 12 P 4 R 5 S 6. We assume that there is no trick in bracketing beyond the ordinary precedence rules and that multiplication and division are performed before addition and subtraction, working from left to right within each precedence level.

Concept / Approach:
The key concept is to first rewrite the coded expression in terms of the actual arithmetic symbols and then apply the usual precedence. If we substitute the correct operations, the expression becomes a standard arithmetic sentence. From there, we simply evaluate step by step, taking care not to change the order of operations.

Step-by-Step Solution:
Step 1: Replace Q by multiplication, P by division, R by addition, and S by subtraction.Step 2: The coded expression 18 Q 12 P 4 R 5 S 6 becomes 18 * 12 / 4 + 5 - 6.Step 3: Apply operation precedence. First handle multiplication and division from left to right: 18 * 12 = 216.Step 4: Now divide 216 by 4 to get 216 / 4 = 54.Step 5: The expression is now 54 + 5 - 6.Step 6: Perform addition and subtraction from left to right: 54 + 5 = 59.Step 7: Next, 59 - 6 = 53.Step 8: Therefore, the final result of the coded expression is 53.

Verification / Alternative check:
We can quickly verify by recalculating the intermediate steps. Multiplying 18 by 12 gives 216, dividing by 4 yields 54, adding 5 gives 59, and subtracting 6 brings the answer to 53. Any other sequencing that respects precedence leads to the same result, confirming that no bracketing has been missed.

Why Other Options Are Wrong:
The value 54 would arise if someone incorrectly stopped after evaluating 18 * 12 / 4 and forgot to process the rest of the expression. The value 57 could appear if the subtraction and addition were combined incorrectly, such as doing 54 + (5 - 2) by mistake. The value 59 corresponds to stopping at 54 + 5 and ignoring the final subtraction. The value 95 would belong to a completely misinterpreted or incorrectly ordered evaluation.

Common Pitfalls:
Students often confuse the order of operations when faced with unfamiliar symbols. It is easy to treat the expression as strictly left to right, which is incorrect. Another pitfall is to misread which letter stands for which operation, especially when there are four different mappings. Carefully rewriting the expression with standard symbols before calculating helps avoid these errors.

Final Answer:
The value of the expression is 53.