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The order of operations is a set of rules that define the sequence in which different operations should be performed to evaluate expressions consistently. Common acronyms for this are PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
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The **order of operations** is a fundamental set of rules in mathematics that defines the correct sequence to evaluate different operations within an expression. This ensures that expressions are interpreted and solved consistently, avoiding ambiguity.
### Selecting the Correct Definition
Among the options you've provided, the most accurate definition is:
- **A set of rules that define the order in which the different operations should be performed so that expressions can be evaluated consistently.**
This definition captures the essence of what the order of operations is intended to achieve in mathematical expressions.
### Common Acronyms for Order of Operations
Several acronyms help remember the order of operations. The most widely recognized ones include:
1. **PEMDAS**:
- **P**: Parentheses
- **E**: Exponents
- **M**: Multiplication
- **D**: Division
- **A**: Addition
- **S**: Subtraction
2. **BODMAS**:
- **B**: Brackets
- **O**: Orders (i.e., powers and roots)
- **D**: Division
- **M**: Multiplication
- **A**: Addition
- **S**: Subtraction
3. **BEDMAS**:
- **B**: Brackets
- **E**: Exponents
- **D**: Division
- **M**: Multiplication
- **A**: Addition
- **S**: Subtraction
The acronym **PEMDAS** is commonly used in the United States, while **BODMAS** is more prevalent in some other English-speaking countries like the United Kingdom and Canada.
### Clarifying "WHEd"
The acronym **"Whed"** does not correspond to any standard order of operations acronym in mathematics. It's possible there was a typo or misunderstanding. If you intended to refer to a specific acronym, please provide more details or check for any possible spelling errors.
### Summary of Order of Operations (PEMDAS/BODMAS)
1. **Parentheses/Brackets**: Solve expressions inside parentheses or brackets first.
2. **Exponents/Orders**: Calculate exponents (powers and roots).
3. **Multiplication and Division**: From left to right.
4. **Addition and Subtraction**: From left to right.
**Example:**
Evaluate the expression:
\[ 3 + 6 \times (5 + 4) \div 3 - 7 \]
**Steps:**
1. **Parentheses**: \(5 + 4 = 9\)
2. **Multiplication**: \(6 \times 9 = 54\)
3. **Division**: \(54 \div 3 = 18\)
4. **Addition and Subtraction**: \(3 + 18 = 21\), then \(21 - 7 = 14\)
**Result:** 14
Understanding and applying the order of operations correctly ensures accurate mathematical calculations and problem-solving.
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