Numeracy

Understanding BODMAS (Order of Operations)




1. What is BODMAS?

BODMAS is an acronym that defines the correct order for solving mathematical expressions:
- Brackets
- Orders (Powers and Square Roots)
- Division
- Multiplication
- Addition
- Subtraction

2. Alternate Terms for BODMAS

  • BIDMAS: Same as BODMAS; "Indices" replaces "Orders".
  • PEMDAS (USA):
  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

3. Applying BODMAS

Step-by-Step Rules

  1. Brackets: Solve expressions inside brackets first.

  2. Example: (4 * (3 + 2) = 20).

  3. Orders: Solve powers or square roots.

  4. Example: (3^2 + 5 = 14).

  5. Division and Multiplication: Perform from left to right.

  6. Example: (6 \div 2 + 7 * 4 = 31).

  7. Addition and Subtraction: Solve from left to right.

  8. Example: (4 + 6 - 7 + 3 = 6).

4. Full Example Using BODMAS

Problem: (4 + 8^2 * (30 \div 5))
1. Brackets: (30 \div 5 = 6). Expression becomes (4 + 8^2 * 6).
2. Orders: (8^2 = 64). Expression becomes (4 + 64 * 6).
3. Multiplication: (64 * 6 = 384). Expression becomes (4 + 384).
4. Addition: (4 + 384 = 388).

Answer: (388).

5. Common Mistakes Avoided with BODMAS

  1. Skipping Brackets: Ignoring brackets leads to incorrect results.

  2. Example: (4 * (3 + 2)) (4 * 3 + 2).

  3. Ignoring Order: Solving addition before division can result in errors.

  4. Example: (6 \div 2 + 7 * 4) solved incorrectly as (6 \div (2 + 7) * 4).

  5. Misapplying Multiplication and Division: These are solved left-to-right, not prioritizing one over the other.

6. Test Questions and Answers

Examples:

  1. (3 + 20 * 3 = 63).
  2. (25 - 5 \div (3 + 2) = 24).
  3. (10 + 6 * (1 + 10) = 76).
  4. (5(3 + 2) + 5^2 = 50).
  5. (7 + 7 \div 7 + 7 * 7 - 7 = 50).

Summing it up

Follow BODMAS carefully to avoid errors, especially with complex expressions. It ensures consistent and accurate results every time!

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