In a coded arithmetic expression, the letters L, M, P and Q stand for different operators as follows: L denotes multiplication, M denotes division, P denotes addition and Q denotes subtraction. What is the numerical value of the expression 16P24M8Q6M2L3 when decoded?

Introduction / Context:
This problem combines coding and arithmetic operations using letters instead of the usual symbols. Each letter corresponds to a standard operator, and you must decode the expression into ordinary arithmetic and then evaluate it correctly. The question tests both decoding skills and accurate application of the order of operations.

Given Data / Assumptions:

• L denotes multiplication (×).
• M denotes division (÷).
• P denotes addition (+).
• Q denotes subtraction (−).
• The coded expression is 16P24M8Q6M2L3.
• After decoding, normal arithmetic precedence holds: multiplication and division before addition and subtraction.

Concept / Approach:
The task is to systematically replace each letter with its corresponding operator, rewrite the entire expression in standard mathematical form and then evaluate it step by step. It is important not to change the order of the numbers, only the operators. Once decoding is done, apply the usual order of operations to find the final value.

Step-by-Step Solution:
Step 1: Write the coded expression clearly: 16P24M8Q6M2L3.Step 2: Replace P with addition. So 16P24 becomes 16 + 24.Step 3: Replace M with division. The first M between 24 and 8 becomes ÷, giving 24 ÷ 8. The second M between 6 and 2 also becomes ÷, giving 6 ÷ 2.Step 4: Replace Q with subtraction, so Q between 8 and 6 becomes −, giving − 6.Step 5: Replace L with multiplication, so L between 2 and 3 becomes ×, giving 2 × 3.Step 6: The fully decoded expression is 16 + 24 ÷ 8 − 6 ÷ 2 × 3.Step 7: Now evaluate using precedence rules. Division and multiplication come first, left to right. Compute 24 ÷ 8 = 3.Step 8: Next compute 6 ÷ 2 = 3, and then 3 × 3 = 9.Step 9: Substitute these values back into the expression to obtain 16 + 3 − 9.Step 10: Finally, perform addition and subtraction from left to right: 16 + 3 = 19, and 19 − 9 = 10.Step 11: Thus, the value of the expression 16P24M8Q6M2L3 is 10.

Verification / Alternative check:
You can check the result by recomputing the expression using a calculator or by grouping the operations slightly differently while still respecting precedence. For example, compute all divisions first, then the multiplication and finally the additions and subtractions. Every correct approach yields the same final value 10, confirming that the decoding and arithmetic steps are correct.

Why Other Options Are Wrong:
The fractional options 13/6 and −1/6 come from misordering the operations or incorrectly combining the division and multiplication parts. The value 14.5 and 9.5 can arise if a student performs operations strictly from left to right or misapplies subtraction instead of division in one segment. None of these correspond to the correctly decoded and evaluated expression, which gives an exact integer value.

Common Pitfalls:
Students often misplace one of the operators when decoding, for example treating M as multiplication instead of division, or they forget to apply the order of operations and compute from left to right. Another frequent error is to stop after partially simplifying the expression. Writing each substitution explicitly and following the precedence step by step avoids these problems.

Final Answer:
After decoding the letters and correctly evaluating the expression, the value of 16P24M8Q6M2L3 is 10.