In a certain code language, "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. What is the value of the expression 45 x 5 - 24 + 3 ÷ 80 when evaluated using these coded operations?

Introduction / Context:
This coded arithmetic problem replaces standard operation symbols with new meanings. Rather than evaluating the expression 45 x 5 - 24 + 3 ÷ 80 directly, you must first decode each symbol to its true operation and then apply normal arithmetic precedence rules. It checks both your ability to follow symbol substitution and your care in performing multi step arithmetic.

Given Data / Assumptions:
- "+" represents multiplication.
- "-" represents addition.
- "x" represents division.
- "÷" represents subtraction.
- The expression to evaluate is 45 x 5 - 24 + 3 ÷ 80.
- After decoding, we apply the usual order of operations: division and multiplication before addition and subtraction.

Concept / Approach:
The solution proceeds in two clear phases. First, interpret each symbol according to the given mapping and rewrite the entire expression in terms of the real operations. Second, evaluate this decoded expression step by step, respecting operator precedence. Any mistake in decoding or precedence leads to an incorrect answer, so discipline in both stages is essential.

Step-by-Step Solution:
Step 1: Original coded expression is 45 x 5 - 24 + 3 ÷ 80. Step 2: Replace "x" by division, "-" by addition, "+" by multiplication, and "÷" by subtraction. Step 3: After substitution, we get: 45 ÷ 5 + 24 * 3 - 80. Step 4: Apply operator precedence. First compute 45 ÷ 5 = 9. Step 5: Then compute 24 * 3 = 72. Step 6: Now perform the remaining operations from left to right: 9 + 72 - 80 = 81 - 80 = 1.

Verification / Alternative check:
To verify, we can quickly redo the substitution and arithmetic. The decoded expression is 45 ÷ 5 + 24 * 3 - 80. Double checking the calculations, 45 ÷ 5 is clearly 9, 24 * 3 is 72, and 9 + 72 = 81. Subtracting 80 gives 1. Since each symbol has been correctly replaced and the calculations are straightforward, the result is stable and trustworthy.

Why Other Options Are Wrong:
- Option 100 would result from incorrect arithmetic such as 9 + 72 + 19 or similar careless combinations.
- Option 52 might appear if someone computed 45 ÷ 5 = 9, then 24 * 3 = 72, but mishandled subtraction or addition.
- Option 82 could come from adding 9 and 72 and then forgetting to subtract 80 properly.

Common Pitfalls:
Many students forget to decode every symbol or accidentally use the printed meaning of the symbol instead of the described one. Another frequent error is to perform operations strictly left to right without prioritizing division and multiplication. Whenever you face such coded arithmetic, always rewrite the whole expression in standard notation first and then calculate carefully.

Final Answer:
After decoding the operators and evaluating with the correct order of operations, the value of the expression is 1.