In a coded operator system, the plus sign means divided by, the minus sign means multiplied by, the cross sign x means minus and the division sign ÷ means plus. Using these meanings, what is the value of the coded expression 16 ÷ 8 - 4 + 2 x 4?

Introduction / Context:
This is an operator substitution problem where familiar arithmetic symbols are assigned new meanings. Instead of directly computing with the visible operators, you must first decode the expression by replacing each symbol with the operation it now represents, and then evaluate the resulting standard arithmetic expression using normal precedence rules.

Given Data / Assumptions:

• The plus sign (+) represents division.
• The minus sign (−) represents multiplication.
• The cross sign x represents subtraction.
• The division sign (÷) represents addition.
• The expression to be evaluated is 16 ÷ 8 - 4 + 2 x 4.
• After decoding, apply the usual order of operations: multiplication and division before addition and subtraction.

Concept / Approach:
We decode each operator according to the given rules, rewrite the entire expression in standard arithmetic and then simplify it step by step. The core reasoning skills tested here are careful reading, systematic substitution and accurate application of arithmetic precedence. Any slip in substitution or order can lead to an incorrect result.

Step-by-Step Solution:
Step 1: Start with the coded expression 16 ÷ 8 - 4 + 2 x 4.Step 2: Replace ÷ with its real meaning, which is addition. So 16 ÷ 8 becomes 16 + 8.Step 3: Replace the minus sign with its real meaning, which is multiplication. So the symbol between 8 and 4 becomes multiplication, turning that segment into 8 * 4.Step 4: Replace the plus sign with its real meaning, which is division. Thus the symbol between 4 and 2 becomes division, giving 4 ÷ 2.Step 5: Replace x with its real meaning, which is subtraction. So 2 x 4 becomes 2 − 4.Step 6: Putting all substitutions together, the decoded expression is 16 + 8 * 4 ÷ 2 − 4.Step 7: According to the order of operations, first compute multiplication and division from left to right. Calculate 8 * 4 = 32.Step 8: Next compute 32 ÷ 2 = 16.Step 9: Substitute back into the expression to get 16 + 16 − 4.Step 10: Now perform the remaining operations from left to right: 16 + 16 = 32, and 32 − 4 = 28.

Verification / Alternative check:
You can verify the answer by directly substituting the real operators in one pass: 16 plus becomes 16 ÷ 8? No, you interpret them as 16 + 8 * 4 ÷ 2 − 4 exactly as in the decoded expression and then recompute. Any attempt to evaluate with the original meanings of the symbols or to calculate left to right without following precedence will yield the wrong result. Repeating the calculation confirms that the decoded value is 28.

Why Other Options Are Wrong:
The option 16 might result if a student misreads the rules and only evaluates 16 ÷ 8 with normal meaning. The option 32 appears if someone decodes correctly but forgets the final subtraction of 4. The option 44 or 24 arise from misordered operations or incorrect substitutions of one or more symbols. Only 28 matches the correctly decoded and properly evaluated expression.

Common Pitfalls:
Frequent errors include using usual operator meanings instead of the coded ones, skipping one substitution, or performing addition and subtraction before finishing all multiplication and division. To avoid these mistakes, write down the fully decoded expression explicitly and then simplify it carefully in stages.

Final Answer:
After decoding the operators and evaluating, the value of the expression 16 ÷ 8 - 4 + 2 x 4 is 28.