Understanding the Operator Substitution

The problem asks us to evaluate a mathematical expression, but with a twist: the standard arithmetic operators (+, -, ×, ÷) have been redefined.

Here are the given operator substitutions:

• '+' represents '÷'
• '-' represents '+'
• '×' represents '-'
• '÷' represents '×'

The original expression is: [{(49×12)-(6÷2)}+(4-3)]÷5

Applying the Operator Substitutions

We need to replace each operator in the original expression with its new meaning according to the rules provided.

1. Replace '×' with '-': The term (49×12) becomes (49 - 12).
2. Replace '÷' with '×': The term (6÷2) becomes (6 × 2).
3. Replace '-' with '+': The term (4-3) becomes (4 + 3).
4. Replace the '-' sign (between the first two terms inside the curly braces) with '+'.
5. Replace the '+' sign (between the curly braces and the last term inside the square brackets) with '÷'.
6. Replace the final '÷' sign outside the square brackets with '×'.

After applying all these substitutions, the expression transforms into:

[ {(49 - 12) + (6 × 2)} ÷ (4 + 3) ] × 5

Step-by-Step Evaluation

Now, we evaluate the transformed expression using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).

1. Evaluate innermost parentheses:
   • (49 - 12) = 37
   • (6 × 2) = 12
   • (4 + 3) = 7
2. Substitute these results back into the expression:

   [ {37 + 12} ÷ 7 ] × 5

3. Evaluate the expression inside the curly braces:

   {37 + 12} = 49

4. Substitute this result back:

   [ 49 ÷ 7 ] × 5

5. Evaluate the expression inside the square brackets:

   49 ÷ 7 = 7

6. Substitute this result back:

   7 × 5

7. Perform the final calculation:

   7 × 5 = 35

Therefore, the value of the given expression after applying the operator substitutions is 35.