If "+" means "÷", "÷" means "-", "-" means "×" and "×" means "+", then what will be the value of the expression 8 + 4 ÷ 3 × 5 - 9 when evaluated under these changed operator meanings?

Introduction / Context:
This is a coded-operations problem where each mathematical symbol has been assigned a new meaning. The numbers in the expression remain the same, but the operators "+", "÷", "-" and "×" no longer represent their usual operations. We must carefully replace each symbol with its true meaning and then evaluate the resulting arithmetic expression to find the correct value.

Given Data / Assumptions:

• "+" means "÷" (division).
• "÷" means "-" (subtraction).
• "-" means "×" (multiplication).
• "×" means "+" (addition).
• The given expression is 8 + 4 ÷ 3 × 5 - 9.
• After decoding the operators, normal precedence rules (multiplication and division before addition and subtraction) must be followed.

Concept / Approach:
The safest method is to rewrite the entire expression using the real operations instead of the coded symbols. For every occurrence of "+", we write "÷"; for every "÷", we write "-"; for every "-", we write "×"; and for every "×", we write "+". Once that translation is complete, we evaluate the new expression step by step, giving priority to multiplication and division, and finally performing addition and subtraction from left to right.

Step-by-Step Solution:
Start with the coded expression: 8 + 4 ÷ 3 × 5 - 9. Replace "+" with "÷" so 8 + 4 becomes 8 ÷ 4. Replace "÷" with "-" so 4 ÷ 3 becomes 4 - 3. Replace "×" with "+" so 3 × 5 becomes 3 + 5. Replace "-" with "×" so 5 - 9 becomes 5 × 9. Putting it all together, the decoded expression is: 8 ÷ 4 - 3 + 5 × 9. Now apply normal precedence: first handle ÷ and ×. Compute 8 ÷ 4 = 2. Compute 5 × 9 = 45. Substitute back: the expression becomes 2 - 3 + 45. Now evaluate from left to right for addition and subtraction. 2 - 3 = -1. Then -1 + 45 = 44. So the final value of the decoded expression is 44.

Verification / Alternative check:
We can verify by quickly re-parsing: only two operations are nontrivial after decoding, 8 ÷ 4 and 5 × 9, which are 2 and 45 respectively. Everything else is simple addition or subtraction. Repeating the calculation gives the same result, which confirms that 44 is robust and not dependent on any hidden assumptions.

Why Other Options Are Wrong:
The values 53, 62 and 64 would appear only if we misinterpreted at least one operator or ignored precedence and evaluated strictly from left to right. For example, treating "+" as plus instead of division or failing to multiply 5 and 9 before adding would lead to an incorrect total. Since our solution carefully follows the given mapping and correct arithmetic rules, these alternatives are incorrect.

Common Pitfalls:
Typical mistakes include replacing operators only partially, forgetting that all occurrences must change, or performing all operations in the written order without respecting precedence. Another frequent error is to mentally mix the coded and real meanings of symbols, which can be avoided by clearly writing the fully decoded expression first.

Final Answer:
Under the changed meanings of the operators, the value of the expression 8 + 4 ÷ 3 × 5 - 9 is 44.