In a certain code language, "+" represents "×", "−" represents "+", "×" represents "÷" and "÷" represents "−". What is the value of 25 + 10 ÷ 240 × 16 under this coding?

Introduction / Context:
This problem belongs to the coded mathematical operations category. The usual symbols for addition, subtraction, multiplication, and division are replaced with different meanings. Your task is to carefully decode each symbol, rewrite the expression using actual operations, and then evaluate the resulting arithmetic expression. These questions check attention to detail, correct use of operator precedence, and the ability to handle symbolic substitutions without confusion.

Given Data / Assumptions:

- In the code language, the symbol "+" means multiplication.
- The symbol "−" means addition, although it does not appear in this particular expression.
- The symbol "×" means division.
- The symbol "÷" means subtraction.
- The coded expression to evaluate is: 25 + 10 ÷ 240 × 16.
- We assume the usual arithmetic precedence once the expression is decoded: division and multiplication before addition and subtraction, evaluated from left to right at the same level.

Concept / Approach:
The correct approach is to translate each symbol into its real meaning one by one, while preserving the order of numbers. After this translation, we obtain a standard arithmetic expression that can be evaluated using normal rules. It is crucial not to mix up the original symbols with their coded meanings and not to apply the coded operations directly on the original expression without first rewriting it.

Step-by-Step Solution:
Step 1: Replace each symbol with its true operation. "+" represents "×", so 25 + 10 becomes 25 × 10. "÷" represents "−", so 10 ÷ 240 becomes 10 − 240. "×" represents "÷", so 240 × 16 becomes 240 ÷ 16. The fully decoded expression is: 25 × 10 − 240 ÷ 16. Step 2: Apply operator precedence. First compute the multiplication: 25 × 10 = 250. Then compute the division: 240 ÷ 16 = 15. Now the expression becomes: 250 − 15. Step 3: Perform the final subtraction. 250 − 15 = 235.

Verification / Alternative check:
We can quickly verify by re-reading the code mapping. If "+" were misread as addition instead of multiplication, we would obtain a completely different expression and answer. Similarly, if "÷" were misread as division rather than subtraction, the second operation would be incorrect. Confirming that each symbol translation aligns exactly with the problem statement and redoing the arithmetic confirms that 235 is stable as the correct value.

Why Other Options Are Wrong:
Option 85 would arise if a student divided 240 by 16 first and then used an incorrect combination of operations, perhaps treating "+" as addition and "÷" as division. Option 12 or 20 may appear if the order of operations is ignored and the expression is evaluated strictly left to right or if some of the coded meanings are mixed up. None of these approaches respect both the correct mapping and the standard precedence rules, so they lead to wrong results.

Common Pitfalls:
Typical mistakes include applying the code backwards (for example, using "+" as addition instead of multiplication), forgetting to respect operator precedence after decoding, or partially decoding the expression and then trying to evaluate it in an inconsistent way. Students should always rewrite the entire expression using normal symbols first and only then perform arithmetic.

Final Answer:
After decoding the expression and evaluating it correctly, the value of 25 + 10 ÷ 240 × 16 is 235.