If the usual arithmetic symbols are replaced as follows: "×" means addition, "÷" means subtraction, "+" means multiplication and "−" means division, then what is the numerical value of 20 × 8 ÷ 8 − 4 + 2?

Introduction / Context:
This is a coded-operations question, where each arithmetic symbol is given a new meaning. To evaluate the expression correctly, we must first decode every symbol into the real operation it now represents, and then apply the standard order of operations. Such questions check both attention to detail and fluency with operator precedence rules.

Given Data / Assumptions:

• "×" stands for addition.
• "÷" stands for subtraction.
• "+" stands for multiplication.
• "−" stands for division.
• Expression: 20 × 8 ÷ 8 − 4 + 2.
• Standard precedence still applies after decoding: multiplication and division before addition and subtraction.

Concept / Approach:
We translate the given coded expression into a normal arithmetic expression with the correct operations. After substitution, we carefully perform division and multiplication first, followed by addition and subtraction. It is crucial not to change the order of numbers, only the meanings of the symbols between them.

Step-by-Step Solution:
Rewrite each symbol: "×" becomes +, "÷" becomes −, "−" becomes ÷, and "+" becomes ×.Thus, 20 × 8 ÷ 8 − 4 + 2 becomes 20 + 8 − 8 ÷ 4 × 2.Now apply precedence: compute 8 ÷ 4 × 2 first. Since division and multiplication have the same rank, we go left to right: 8 ÷ 4 = 2, then 2 × 2 = 4.Substitute this back: 20 + 8 − 4. Now evaluate from left to right: 20 + 8 = 28 and 28 − 4 = 24.

Verification / Alternative check:
We can recheck by writing the decoded expression explicitly as 20 + 8 - (8 / 4) * 2 to avoid confusion and confirm that 8 / 4 = 2 and 2 * 2 = 4, so the final calculation remains 20 + 8 - 4 = 24.Trying to evaluate with the old meanings of the symbols would give a completely different and incorrect result, so the decoding step is absolutely essential.

Why Other Options Are Wrong:
80 or 25 would arise only if the new operator meanings were ignored or misapplied, especially if one incorrectly treats the expression as 20 × 8 = 160 and then adjusts later.A result of 5 might come from wrong grouping or mixing up the order in which multiplication and division are handled after decoding.

Common Pitfalls:
Students often apply the new meanings inconsistently, forgetting to change one of the symbols in the middle of the expression.Another common error is to assume that the leftmost operation must be performed first, ignoring the higher precedence of multiplication and division.

Final Answer:
After decoding the symbols and evaluating with correct precedence, the value of the expression is 24.