If "-" means "added to", "+" means "divided by", "÷" means "multiplied by" and "x" means "subtracted from", then what is the value of 13 + 12 x 9 ÷ 3 – 6?

Introduction / Context:
This is a coded operations question that also involves fractional arithmetic. The four arithmetic symbols each stand for a different real operation. After decoding, the resulting expression includes divisions that lead to fractions. The challenge is to convert the coded expression correctly, follow the order of operations and handle fraction calculations without error.

Given Data / Assumptions:

• "-" means "added to", so it represents "+".
• "+" means "divided by", so it represents "/".
• "÷" means "multiplied by", so it represents "*".
• "x" means "subtracted from", so it represents "-".
• The coded expression is 13 + 12 x 9 ÷ 3 – 6.
• After decoding, we still respect the usual precedence: multiplication and division first, then addition and subtraction.

Concept / Approach:
We translate each symbol into its real operation, keeping the numbers in their original sequence. Thus "+" becomes "/", "x" becomes "-", "÷" becomes "*", and "–" becomes "+". Then we evaluate the resulting fractional expression. When we meet divisions that do not yield whole numbers, we keep them as fractions and simplify carefully to avoid rounding errors.

Step-by-Step Solution:
Step 1: Replace each coded operator with its real meaning in 13 + 12 x 9 ÷ 3 – 6. "+" becomes "/", "x" becomes "-", "÷" becomes "*", and "–" becomes "+". Step 2: The decoded expression becomes 13 / 12 - 9 * 3 + 6. Step 3: Follow precedence. First handle multiplication: 9 * 3 = 27. Step 4: Now the expression is 13 / 12 - 27 + 6. Step 5: Combine the integer terms: -27 + 6 = -21. Step 6: Now the expression is 13 / 12 - 21. Step 7: Write -21 as a fraction with denominator 12: -21 = -21 * 12 / 12 = -252 / 12. Step 8: Combine fractions: 13 / 12 - 252 / 12 = (13 - 252) / 12 = -239 / 12.

Verification / Alternative check:
We can verify by approximating decimals: 13 / 12 is approximately 1.0833, and -21 is exactly -21. Thus 1.0833 - 21 ≈ -19.9167. Converting -239 / 12 to decimal gives -239 ÷ 12 ≈ -19.9167, which matches perfectly. This confirms that the fraction -239 / 12 is correct.

Why Other Options Are Wrong:
-117/11 and 117/11 correspond to different fractional values that would arise from incorrect decoding of one or more operators or from mixing up the order of operations. -237/12 also looks similar to the correct answer but differs by 2 / 12, indicating a small arithmetic slip in the numerator. The option 0 would require the positive and negative parts to cancel exactly, which does not happen here.

Common Pitfalls:
Typical errors include treating "+" as usual addition instead of division, and "x" as multiplication instead of subtraction. Another frequent problem is trying to handle decimals mentally instead of working with exact fractions, which can cause rounding mistakes. Writing all fractional steps explicitly with a common denominator helps maintain accuracy.

Final Answer:
After decoding the operators and simplifying the fractional expression, the value of 13 + 12 x 9 ÷ 3 – 6 is -239/12.