Order of Operations (BODMAS / PEMDAS)
When an expression contains many operations — addition, subtraction, multiplication, division, powers, and brackets — the order of operations tells us what to calculate first.
Without a fixed order, the same expression could give different answers. That is why this rule exists and why it is extremely important for school mathematics, competitive exams, daily calculations, and computing.
Why Order of Operations Is Necessary
Consider this expression:
6 + 2 × 3
If we add first:
→ (6 + 2) × 3 = 24
If we multiply first:
→ 6 + (2 × 3) = 12
Two different answers — which one is correct?
To avoid confusion, mathematics follows a fixed universal order.
BODMAS Rule (Used Widely)
BODMAS tells the correct order:
| Letter | Meaning | What to Do |
| B | Brackets | Solve inside brackets first |
| O | Orders | Powers and roots |
| D | Division | Left to right |
| M | Multiplication | Left to right |
| A | Addition | Left to right |
| S | Subtraction | Left to right |
Important: Division and multiplication have equal priority, and so do addition and subtraction. They are done from left to right.
PEMDAS Rule (Same Meaning, Different Name)
PEMDAS is commonly used in some countries:
- P → Parentheses
- E → Exponents
- M → Multiplication
- D → Division
- A → Addition
- S → Subtraction
BODMAS and PEMDAS mean the same thing. Only the naming is different.
Important Clarification (Very Common Mistake)
Many students think multiplication always comes before division. That is wrong.
Example:
8 ÷ 4 × 2
Correct method (left to right):
8 ÷ 4 = 2 2 × 2 = 4
Final Answer: 4
Step-by-Step Solving Method
Follow these steps every time:
- Solve brackets
- Solve powers and roots
- Move left to right for × and ÷
- Move left to right for + and −
Never jump steps.
Worked Examples (Must-Understand)
Example 1
10 + 6 × 2
Step 1: Multiplication → 6 × 2 = 12 Step 2: Addition → 10 + 12 = 22
Answer: 22
Example 2
(10 + 6) × 2
Step 1: Brackets → 10 + 6 = 16 Step 2: Multiplication → 16 × 2 = 32
Answer: 32
Example 3 (With Powers)
5 + 2² × 3
Step 1: Power → 2² = 4 Step 2: Multiplication → 4 × 3 = 12 Step 3: Addition → 5 + 12 = 17
Answer: 17
Brackets Inside Brackets
Always solve the innermost bracket first.
Example:
6 + [2 × (3 + 1)]
Step 1: (3 + 1) = 4 Step 2: 2 × 4 = 8 Step 3: 6 + 8 = 14
Answer: 14
Order of Operations in Daily Life
- Shopping bills (tax before total)
- Cooking recipes (ratios and steps)
- Construction measurements
- Fuel cost calculations
Doing calculations in the wrong order leads to wrong decisions.
Order of Operations in Exams
Competitive exams often include:
- Bracket traps
- Negative number traps
- Division–multiplication confusion
- Power precedence tricks
Speed comes from discipline, not shortcuts.
Order of Operations in Computing
- Programming expressions
- Spreadsheet formulas
- Scientific calculators
Computers strictly follow operator precedence rules. Humans must too.
Practice Questions
Q1. Solve: 12 − 4 × 2
Q2. Solve: (8 + 4) ÷ 2
Q3. Solve: 6 + 18 ÷ 3 × 2
Quick Quiz
Q1. Which comes first: multiplication or division?
Q2. Solve quickly: 3 + 3² × 2
Quick Recap
- Order of operations avoids ambiguity
- BODMAS and PEMDAS mean the same
- Brackets and powers come first
- Equal priority operators go left to right
- Used everywhere: exams, life, computing