Solving Math Expressions with Operator Substitution

This question involves evaluating a mathematical expression where the standard arithmetic operators (+, -, ×, ÷) have been assigned new meanings. We need to apply these new rules and follow the order of operations (BODMAS/PEMDAS) to find the correct answer.

Understanding the Operator Substitution Rules

The problem provides the following substitutions:

• The symbol $+$ actually means multiplication ($×$).
• The symbol $÷$ actually means subtraction ($-$).
• The symbol $-$ actually means division ($÷$).
• The symbol $×$ actually means addition ($+$).

Applying the Substitutions to the Expression

The original expression is:

$150 \times 25 - 5 \div 10 + 2$

Now, let's substitute the operators according to the given rules:

• Replace $×$ with $+$
• Replace $-$ with $÷$
• Replace $÷$ with $-$
• Replace $+$ with $×$

Applying these changes, the expression becomes:

$150 + 25 \div 5 - 10 \times 2$

Evaluating the New Expression using BODMAS

We follow the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) to evaluate the expression:

1. Division: First, perform the division. $25 \div 5 = 5$ The expression now is: $150 + 5 - 10 \times 2$
2. Multiplication: Next, perform the multiplication. $10 \times 2 = 20$ The expression now is: $150 + 5 - 20$
3. Addition: Perform addition from left to right. $150 + 5 = 155$ The expression now is: $155 - 20$
4. Subtraction: Finally, perform the subtraction. $155 - 20 = 135$

Final Result

After applying the operator substitutions and following the BODMAS order of operations, the value of the expression is 135.