If \(+\) means \(\times\), \(\div\) means- , - means \(\div\) then, and \(\times\) means \(+\), then
what is \(150\times25-5\div10+2\)?
135
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:
- Division: First, perform the division. $25 \div 5 = 5$ The expression now is: $150 + 5 - 10 \times 2$
- Multiplication: Next, perform the multiplication. $10 \times 2 = 20$ The expression now is: $150 + 5 - 20$
- Addition: Perform addition from left to right. $150 + 5 = 155$ The expression now is: $155 - 20$
- 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.
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