Understanding Symbol Substitution for Expression Evaluation

This problem requires us to evaluate a mathematical expression where the standard arithmetic symbols have been given new meanings. We need to carefully substitute the symbols based on the provided rules and then calculate the result using the correct order of operations.

The given rules for symbol substitution are:

• '+' represents subtraction (-)
• '−' represents multiplication (*)
• '÷' represents addition (+)
• '×' represents division (/)

The original expression is: 14 − 19 + 240 × 16 ÷ 61

Applying the substitution rules to the expression, we get:

14 * 19 - 240 / 16 + 61

Now, we need to find the value of this new expression.

Evaluating the Substituted Expression Step-by-Step

To evaluate the expression 14 * 19 - 240 / 16 + 61, we follow the standard order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division and Multiplication from left to right, Addition and Subtraction from left to right).

1. Multiplication: First, we perform the multiplication operation.

   \(14 \times 19 = 266\)

2. Division: Next, we perform the division operation.

   \(240 / 16 = 15\)

3. Substitute results: Now, replace the multiplication and division parts in the expression with their calculated values:

   266 - 15 + 61

4. Subtraction: Perform the subtraction operation (working from left to right).

   \(266 - 15 = 251\)

5. Addition: Finally, perform the addition operation.

   \(251 + 61 = 312\)

Final Result of the Expression

After performing all the operations in the correct order, the value of the expression 14 × 19 - 240 / 16 + 61 is 312.

Therefore, the value of the original expression 14 − 19 + 240 × 16 ÷ 61 after applying the given symbol substitutions is 312.