If "+" means "minus", "×" means "divided by", "÷" means "plus" and "−" means "multiplied by", then what is the value of 38 × 2 − 6 + 19 ÷ 35?

Introduction / Context:
This question uses a substitution code for arithmetic symbols. Each familiar operator sign is reassigned a new meaning, and you must decode the expression before you can evaluate it. The goal is to check whether the learner can carefully translate and then correctly apply the rules of arithmetic without being misled by the usual appearance of the symbols.

Given Data / Assumptions:

- "+" now means subtraction (minus).
- "×" now means division.
- "÷" now means addition.
- "−" now means multiplication.
- The coded expression is: 38 × 2 − 6 + 19 ÷ 35.
- After decoding, we use normal arithmetic precedence: division and multiplication first, followed by addition and subtraction from left to right.

Concept / Approach:
The method is straightforward. First, translate each coded symbol into its actual arithmetic operation while keeping the order of the numbers unchanged. This converts the coded expression into a standard numerical expression. Then, evaluate step by step, ensuring that multiplication and division are handled before addition and subtraction, just as in standard BODMAS or PEMDAS rules.

Step-by-Step Solution:
Step 1: Decode each symbol. "×" means "divided by", so 38 × 2 becomes 38 ÷ 2. "−" means "multiplied by", so − 6 becomes × 6. "+" means "minus", so + 19 becomes − 19. "÷" means "plus", so 19 ÷ 35 becomes 19 + 35. Putting this together, the full decoded expression is: 38 ÷ 2 × 6 − 19 + 35. Step 2: Apply division and multiplication from left to right. 38 ÷ 2 = 19. Then 19 × 6 = 114. Now the expression reduces to: 114 − 19 + 35. Step 3: Perform the remaining addition and subtraction from left to right. 114 − 19 = 95. 95 + 35 = 130.

Verification / Alternative check:
Rechecking the symbol mapping confirms that there is no ambiguity. The converted expression 38 ÷ 2 × 6 − 19 + 35 is standard arithmetic. A quick mental check shows that 38 ÷ 2 is 19, and 19 × 6 is 114, which makes our intermediate steps reliable. Finally, subtracting 19 and adding 35 gives 130, which fits cleanly with the available options and uses all the numbers exactly once, confirming consistency.

Why Other Options Are Wrong:
An answer like 140 or 135 would typically result from either ignoring operator precedence or misreading one of the coded symbols, for example, treating "+" as addition instead of subtraction or forgetting that "−" indicates multiplication. Option 145 would similarly require incorrect ordering of operations or mixing up addition and subtraction after the initial computations. Since none of these alternatives respect both the substitutions and the precedence rules, they cannot be correct.

Common Pitfalls:
Students may be tempted to solve the expression as written, with the old meanings of the symbols, which will give a completely different result. Another common error is decoding the operations correctly but then evaluating strictly from left to right without giving priority to division and multiplication. To avoid these mistakes, always rewrite the coded expression fully using real operations first, then apply standard arithmetic rules.

Final Answer:
The correctly decoded and evaluated value of 38 × 2 − 6 + 19 ÷ 35 is 130.