BODMAS/PEMDAS rule — order of operations with tricky examples

Question

Explain the BODMAS/PEMDAS rule for order of operations. Solve: $8 + 2 \times 5$ , $24 \div 6 - 2 + 3$ , and $(3 + 5) \times 2 - 4 \div 2$ .

Solution — Step by Step

BODMAS stands for: Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction.

Alternatively, PEMDAS: Parentheses → Exponents → Multiplication → Division → Addition → Subtraction.

Both are the same rule. Division and multiplication have equal priority (solve left to right). Addition and subtraction also have equal priority (left to right).

Problem 1: $8 + 2 \times 5$

Multiplication before addition: $2 \times 5 = 10$ , then $8 + 10 = \mathbf{18}$

(NOT $(8 + 2) \times 5 = 50$ — that would be wrong without brackets.)

Problem 2: $24 \div 6 - 2 + 3$

Division first: $24 \div 6 = 4$ . Then left to right: $4 - 2 + 3 = 2 + 3 = \mathbf{5}$

Problem 3: $(3 + 5) \times 2 - 4 \div 2$

Brackets first: $3 + 5 = 8$ . Then multiplication and division (left to right): $8 \times 2 = 16$ and $4 \div 2 = 2$ . Finally: $16 - 2 = \mathbf{14}$

flowchart TD
    A[BODMAS Priority] --> B[1. Brackets first]
    B --> C[2. Orders - powers, roots]
    C --> D[3. Division and Multiplication - left to right]
    D --> E[4. Addition and Subtraction - left to right]

Why This Works

Without a fixed order, the same expression would give different answers depending on which operation you do first. BODMAS is a convention that everyone agrees on, so there is exactly one correct answer for every expression.

Common Mistake

The biggest mistake: thinking multiplication ALWAYS comes before division (because M comes before D in BODMAS). Actually, multiplication and division have equal priority — we solve them left to right. Same for addition and subtraction. Example: $12 \div 3 \times 2 = 4 \times 2 = 8$ (left to right), NOT $12 \div 6 = 2$ .

When in doubt, add brackets to make the order clear. Writing $(12 \div 3) \times 2$ removes all ambiguity. Examiners love testing expressions where left-to-right order matters.

Question

Solution — Step by Step

Why This Works

Common Mistake

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