In a certain code language, the symbol plus represents division, minus represents multiplication, the cross symbol represents subtraction and the division sign represents addition. What is the numerical value of the coded expression 16 ÷ 84 + 2 x 4 when it is decoded using these meanings?

Introduction / Context:
This coding and decoding question tests how well you can reinterpret arithmetic expressions when the usual operators are given new meanings. Instead of performing the operations that the symbols normally represent, you must carefully replace each symbol with its given meaning and then evaluate the expression using standard arithmetic rules and the conventional order of operations.

Given Data / Assumptions:

• The symbol plus (+) stands for division.
• The symbol minus (−) stands for multiplication.
• The symbol cross (x) stands for subtraction.
• The division sign (÷) stands for addition.
• The expression to be decoded is 16 ÷ 84 + 2 x 4.
• After decoding, operations follow the normal precedence: division and multiplication before addition and subtraction.

Concept / Approach:
The key idea is to replace each coded symbol with its real meaning, convert the entire expression into a standard arithmetic form and then evaluate it correctly. Many students lose marks in this type of question either by directly calculating with the visible symbols or by ignoring the correct order of operations, so a careful, stepwise approach is essential.

Step-by-Step Solution:
Step 1: Write the coded expression: 16 ÷ 84 + 2 x 4.Step 2: Replace ÷ with its real meaning, which is addition. So 16 ÷ 84 becomes 16 + 84.Step 3: Replace + with its real meaning, which is division. So the part 84 + 2 becomes 84 ÷ 2.Step 4: Replace x with its real meaning, which is subtraction. So 2 x 4 becomes 2 − 4.Step 5: The fully decoded expression is 16 + 84 ÷ 2 − 4.Step 6: Apply the order of operations. First calculate 84 ÷ 2 = 42.Step 7: Substitute back to get 16 + 42 − 4.Step 8: Now perform left to right addition and subtraction: 16 + 42 = 58, then 58 − 4 = 54.Step 9: Therefore, the value of the coded expression is 54.

Verification / Alternative check:
You can quickly verify the answer by redoing the decoding in one pass. Replace each operator in 16 ÷ 84 + 2 x 4 with its real meaning to directly get 16 + 84 ÷ 2 − 4. Evaluating this again by first doing 84 ÷ 2 = 42 and then 16 + 42 − 4 gives 54. The repeated calculation confirms that there is no mistake in decoding the operators or in the arithmetic steps.

Why Other Options Are Wrong:
The option 44 could arise if someone miscalculates 84 ÷ 2 as 32 or subtracts incorrectly at the end. The option 48 might appear if the student forgets to subtract 4 or decodes one of the symbols wrongly. The option 58 is what you obtain if you decode correctly but forget the final subtraction. The option 60 could come from incorrectly performing addition before division or from some other incorrect intermediate step. None of these match the carefully evaluated result of 54.

Common Pitfalls:
A very common mistake is to treat the symbols as if they had their usual meanings instead of the coded meanings. Another frequent error is ignoring the order of operations and calculating from left to right without handling division before addition and subtraction. Calculation slips when dividing 84 by 2 or subtracting 4 at the end also lead to wrong answers. Carefully decoding each operator and then strictly following the arithmetic precedence avoids these traps.

Final Answer:
The correctly decoded and evaluated value of the expression is 54.