If '+' means '÷', '-' means '+', '×' means '-', '÷' means '×', then what will come in place of the question mark (?) in the following equation? 320 + 64 - 18 ÷ 2 × 28 = ?
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Understanding Operator Changes
This problem requires us to first understand how the mathematical operators in the given expression are redefined. We are provided with a set of rules that change the meaning of the standard arithmetic symbols.
- The symbol '+' now represents division (÷).
- The symbol '-' now represents addition (+).
- The symbol '×' now represents subtraction (-).
- The symbol '÷' now represents multiplication (×).
Rewriting the Expression
Now, we will take the original expression and substitute the operators according to the rules given:
Original Expression: \(320 + 64 - 18 ÷ 2 × 28 = ?\)
Let's replace the operators:
- '+' becomes '÷'
- '-' becomes '+'
- '÷' becomes '×'
- '×' becomes '-'
Substituting these into the expression, we get the new expression:
New Expression: \(320 ÷ 64 + 18 × 2 - 28 = ?\)
Solving the Expression using BODMAS/PEMDAS
To solve the new expression, we need to follow the standard order of operations, commonly known as BODMAS or PEMDAS.
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's apply BODMAS to our new expression: \(320 ÷ 64 + 18 × 2 - 28\)
Step 1: Division
First, perform the division operation:
\(320 ÷ 64 = 5\)
The expression now becomes:
\(5 + 18 × 2 - 28\)
Step 2: Multiplication
Next, perform the multiplication operation:
\(18 × 2 = 36\)
The expression now becomes:
\(5 + 36 - 28\)
Step 3: Addition and Subtraction (from left to right)
Now, perform the addition and subtraction from left to right.
Perform addition first:
\(5 + 36 = 41\)
The expression is now:
\(41 - 28\)
Finally, perform the subtraction:
\(41 - 28 = 13\)
So, the value of the expression is 13.
| Step | Operation | Calculation | Remaining Expression |
|---|---|---|---|
| 1 | Division | \(320 ÷ 64 = 5\) | \(5 + 18 × 2 - 28\) |
| 2 | Multiplication | \(18 × 2 = 36\) | \(5 + 36 - 28\) |
| 3 | Addition | \(5 + 36 = 41\) | \(41 - 28\) |
| 4 | Subtraction | \(41 - 28 = 13\) | \(13\) |
Revision Table: Operator Swapping Basics
| Original Symbol | New Meaning |
|---|---|
| + | ÷ |
| - | + |
| × | - |
| ÷ | × |
Additional Information: Order of Operations (BODMAS/PEMDAS)
The order of operations is crucial when evaluating mathematical expressions involving multiple operations. Failing to follow the correct order will lead to an incorrect result.
BODMAS/PEMDAS helps ensure everyone gets the same answer for the same expression. It standardizes the calculation process.
Remember: Division and Multiplication have the same priority and are performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have the same priority and are performed from left to right.
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