In a certain code language, the symbols are redefined so that "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using this coding, what is the value of 56 ÷ 8 + 12 - 72?

Introduction / Context:
This coding decoding question tests your comfort with operator substitution. The arithmetic symbols do not carry their usual meanings. Instead, each symbol stands for another operation, and you must correctly translate the coded expression into a standard arithmetic expression before evaluating it. Such problems reward careful reading and strict adherence to the new definitions.

Given Data / Assumptions:

• "+" represents multiplication.
• "-" represents addition.
• "x" represents division.
• "÷" represents subtraction.
• Coded expression: 56 ÷ 8 + 12 - 72.
• Standard operator precedence (multiplication and division before addition and subtraction) still applies after decoding.

Concept / Approach:
The correct approach is twofold. First, substitute each symbol in the given expression with the real operation it stands for. Second, evaluate the resulting normal arithmetic expression using correct precedence. It is important not to mix up the meaning of the symbols, as even a single mistake in substitution will give a completely different result.

Step-by-Step Solution:
Step 1: Start with the coded expression: 56 ÷ 8 + 12 - 72.Step 2: Replace each symbol by its actual meaning: "÷" becomes subtraction, "+" becomes multiplication, "-" becomes addition.Step 3: After substitution we get: 56 - 8 * 12 + 72.Step 4: Evaluate multiplication first: 8 * 12 = 96, so the expression becomes 56 - 96 + 72.Step 5: Now compute from left to right for addition and subtraction: 56 - 96 = -40, and -40 + 72 = 32.

Verification / Alternative check:
We can quickly check that we did not misread any code. There is no "x" symbol in the expression, so no division is involved. Only one multiplication, 8 * 12, appears after decoding. Repeating the calculation confirms that the final value is 32. Therefore the answer is consistent and robust against minor arithmetic slips.

Why Other Options Are Wrong:

• 88 and 82 could arise from evaluating strictly left to right or from misplacing the multiplication.
• 44 might appear if someone mistakenly computes (56 - 8) * (12 + 72) or ignores precedence.
• 56 would be obtained only if the middle terms cancelled each other incorrectly, which they do not.

Common Pitfalls:
The most common pitfalls are forgetting to apply operator precedence after decoding and mixing up which symbol stands for which operation. Some candidates also mistakenly treat the coded expression as if it used normal operators, which leads to completely different values. Always decode first, then calculate carefully.

Final Answer:
After decoding and simplifying, the value of 56 ÷ 8 + 12 - 72 is 32.