Solving Mathematical Operations with Symbol Substitution

This question requires us to substitute the standard mathematical symbols with new operations as defined and then evaluate the given expression following the order of operations (BODMAS/PEMDAS).

Let's first understand the given symbol substitutions:

• The symbol × means 'Minus' (–).
• The symbol ÷ means 'Multiplied by' (×).
• The symbol – means 'Plus' (+).
• The symbol + means 'Divided by' (÷).

The given expression is:

\(16 \div 8 \times 4 - 8 + 4\)

Now, we substitute the original symbols with the new operations based on the rules provided:

• Replace ÷ with ×
• Replace × with –
• Replace – with +
• Replace + with ÷

After substituting the symbols, the expression becomes:

\(16 \times 8 - 4 + 8 \div 4\)

Now, we solve this new expression using the order of operations (BODMAS/PEMDAS):

1. Division: Perform division first.

   \(8 \div 4 = 2\)

   The expression is now: \(16 \times 8 - 4 + 2\)

2. Multiplication: Perform multiplication next.

   \(16 \times 8 = 128\)

   The expression is now: \(128 - 4 + 2\)

3. Addition and Subtraction: Perform addition and subtraction from left to right.

   First, subtraction: \(128 - 4 = 124\)

   The expression is now: \(124 + 2\)

   Next, addition: \(124 + 2 = 126\)

So, the final value of the expression \(16 \div 8 \times 4 - 8 + 4\), after applying the given symbol substitutions, is 126.