Order of Operations (PEMDAS/BODMAS) • Topic 1 of 1

PEMDAS/BODMAS Rules

Why Order Matters:

3 + 4 × 2 = ?

If you add first: (3+4)×2 = 7×2 = 14 If you multiply first: 3+(4×2) = 3+8 = 11 Which is correct? MULTIPLY first!

PEMDAS (USA) / BODMAS (UK):

LetterStands ForMeaning
P / BParentheses / BracketsDo inside ( ) first
E / OExponents / OrdersPowers and roots
M / DMultiplication / DivisionLeft to right
D / MDivision / MultiplicationLeft to right
A / SAddition / SubtractionLeft to right

Remember: Please Excuse My Dear Aunt Sally

PEMDAS ORDER OF OPERATIONS:

    ┌─────────────────────────────────────┐
    │                                     │
    │     P     PARENTHESES (Highest)     │
    │     E     EXPONENTS                 │
    │     M     MULTIPLICATION            │
    │     D     DIVISION                  │
    │     A     ADDITION                  │
    │     S     SUBTRACTION (Lowest)      │
    │                                     │
    └─────────────────────────────────────┘

DECISION TREE FOR SOLVING:

    Start: Look for parentheses
                │
                ▼
           Solve inside ( )
                │
                ▼
          Look for exponents
                │
                ▼
          Multiply or Divide
         (left to right)
                │
                ▼
          Add or Subtract
         (left to right)
                │
                ▼
              Answer!


EXAMPLE WORKFLOW: 3 + 4 × (5 - 2)²

    Step 1: Parentheses: 5 - 2 = 3
           3 + 4 × 3²
    
    Step 2: Exponent: 3² = 9
           3 + 4 × 9
    
    Step 3: Multiply: 4 × 9 = 36
           3 + 36
    
    Step 4: Add: 3 + 36 = 39
    
    Answer: 39
Solved Examples
1
Worked Example

Solve 8 + 2 × 5

Solution
  • Multiplication first: 2 × 5 = 10
  • Then add: 8 + 10 = 18
  • Answer: 18
2
Worked Example

Solve (12 - 4) ÷ 2 + 3

Solution
  • Parentheses: 12 - 4 = 8
  • Division: 8 ÷ 2 = 4
  • Addition: 4 + 3 = 7
  • Answer: 7
3
Worked Example

Solve 20 ÷ 4 × 2

Solution
  • Left to right: 20 ÷ 4 = 5
  • Then: 5 × 2 = 10
  • Answer: 10 (not 20÷(4×2)=20÷8=2.5)

Key Points

  • Parentheses FIRST
  • Exponents NEXT
  • Multiply/Divide LEFT to RIGHT
  • Add/Subtract LEFT to RIGHT
  • Same level operations = go left to right
  • PEMDAS = order of operations
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.In the order of operations, what is done first?
Explanation: Brackets first.
Q2.$2+3\times4=$
Explanation: Multiply first: $2+12$.
Q3.$(2+3)\times4=$
Explanation: Brackets first: $5\times4$.
Q4.Multiplication and division are done:
Explanation: Left to right.
Practice more MCQs → 📝 Assignment · 35 marks