If in a certain code language K means subtracted from, L means divided by, M means added to and D means multiplied by, then what is the value of 96 L 4 K 6 M 11 D 9?

Introduction / Context:
This question involves a symbolic representation of arithmetic operations where letters stand in place of the usual operation signs. We are given a mixed expression using K, L, M, and D and told what each letter means. The challenge is to decode this expression into normal arithmetic and then evaluate it. It reinforces careful reading and proper use of operator precedence.

Given Data / Assumptions:

• K means subtracted from.
• L means divided by.
• M means added to.
• D means multiplied by.
• The expression is 96 L 4 K 6 M 11 D 9.
• Standard rules of arithmetic apply once the decoding is completed.

Concept / Approach:
We interpret each symbol in turn. The letter L stands for division, K stands for subtraction, M stands for addition, and D stands for multiplication. After replacing them with the corresponding mathematical operations, we must evaluate the resulting expression with attention to the hierarchy of operations: division and multiplication first, then addition and subtraction. This ensures that we obtain the correct final value rather than a value based on left to right evaluation alone.

Step-by-Step Solution:
Step 1: Replace L with division, K with subtraction, M with addition, and D with multiplication.Step 2: The coded expression 96 L 4 K 6 M 11 D 9 becomes 96 ÷ 4 − 6 + 11 × 9.Step 3: Apply operator precedence. First evaluate 96 ÷ 4, which equals 24.Step 4: Next compute 11 × 9, which equals 99.Step 5: Substitute these values to get 24 − 6 + 99.Step 6: Perform subtraction and addition from left to right. First 24 − 6 = 18.Step 7: Then 18 + 99 = 117.

Verification / Alternative check:
We may quickly recompute to check for arithmetical errors. Since there are only two high precedence operations and two low precedence operations, the calculation is straightforward. 96 divided by 4 is 24, and 11 times 9 is 99. Adding 99 to 18 gives 117. No other grouping of operations is allowed by standard precedence, so 117 is the unique correct result after decoding.

Why Other Options Are Wrong:
The option 125 might result from adding instead of subtracting 6 or miscomputing one of the intermediate results. The values 120 and 145 represent what happens when the operations are taken in the wrong order or the multiplication step is misapplied. The distractor 111 could come from miscalculating 96 divided by 4 as 23 instead of 24. All of these values are inconsistent with a careful reading of the coded operations and correct arithmetic.

Common Pitfalls:
Common mistakes include misinterpreting phrases such as subtracted from, which might tempt a reversal of the operands. In this expression, however, we treat K simply as the standard subtraction operator in the written order. Another frequent error is to ignore the multiplication and division precedence and do the operations from left to right. Writing the decoded expression clearly with all standard symbols helps to prevent these errors.

Final Answer:
After correctly decoding and evaluating 96 L 4 K 6 M 11 D 9, the value of the expression is 117.