PEMDAS or BODMAS which one is correct acronym for order of operations?

Both PEMDAS and BODMAS are correct acronyms for the order of operations, but they are used in different regions. They essentially describe the same mathematical principles:

- **PEMDAS** is commonly used in the United States.
  - **P**: Parentheses
  - **E**: Exponents
  - **MD**: Multiplication and Division (from left to right)
  - **AS**: Addition and Subtraction (from left to right)

- **BODMAS** is commonly used in the United Kingdom and other countries.
  - **B**: Brackets
  - **O**: Orders (i.e., exponents)
  - **DM**: Division and Multiplication (from left to right)
  - **AS**: Addition and Subtraction (from left to right)

The order of operations is the same in both acronyms:

1. **Parentheses/Brackets**: Solve expressions inside parentheses or brackets first.
2. **Exponents/Orders**: Evaluate exponents or orders next.
3. **Multiplication and Division**: Perform multiplication and division from left to right.
4. **Addition and Subtraction**: Finally, perform addition and subtraction from left to right.

### Example to illustrate the order of operations:

Given the expression: \( 3 + 6 \times (5 + 4) \div 3^2 \),

1. **Parentheses/Brackets**:
   \[
   5 + 4 = 9
   \]
   The expression now becomes \( 3 + 6 \times 9 \div 3^2 \).

2. **Exponents/Orders**:
   \[
   3^2 = 9
   \]
   The expression now becomes \( 3 + 6 \times 9 \div 9 \).

3. **Multiplication and Division** (from left to right):
   \[
   6 \times 9 = 54
   \]
   The expression now becomes \( 3 + 54 \div 9 \).
   
   \[
   54 \div 9 = 6
   \]
   The expression now becomes \( 3 + 6 \).

4. **Addition and Subtraction** (from left to right):
   \[
   3 + 6 = 9
   \]

Therefore, the final result is \( 9 \).

Would you like more details or have any questions about this topic?

### Here are some related questions you might want to ask:
1. What are some common mistakes when applying the order of operations?
2. How does the order of operations work with nested parentheses or brackets?
3. Can you explain how the order of operations applies to algebraic expressions?
4. What happens if you ignore the order of operations in a calculation?
5. Are there any differences in the order of operations for different types of mathematical problems?

### Tip:

When using the order of operations, always work from the innermost parentheses or brackets outwards, and ensure each step is carefully followed to avoid mistakes.

Understand the differences between PEMDAS and BODMAS and learn how they describe the order of operations in mathematics. Both acronyms outline the sequence of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), and Addition and Subtraction (left to right). Example included.

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