Order of Operations

Why Do We Need an Order?

If everyone solved a calculation in a different order, they would get different answers! Look at \(2 + 3 \times 4\):

❌ Left to right: \(2 + 3 = 5\), then \(5 \times 4 = 20\)

✅ Correct order: \(3 \times 4 = 12\), then \(2 + 12 = 14\)

To make sure everyone gets the same answer, we always follow the same order. Two popular ways to remember it are PEMDAS and BODMAS — they mean exactly the same thing.

P/B

Parentheses / Brackets — do anything inside \(( \; )\) first.

E/O

Exponents / Orders — powers and roots like \(3^2\) or \(\sqrt{9}\).

Multiplication & Division — left to right (they are equal rank).

Addition & Subtraction — left to right (they are equal rank).

PEMDAS

Parentheses Exponents Multiply / Divide Add / Subtract

BODMAS

Brackets Orders Divide / Multiply Add / Subtract

Watch Out!

× and ÷ are equal + and − are equal

When operations are equal rank, work left to right.

Worked Example

Evaluate \(6 + 2 \times (3^2 - 4)\)

1. Parentheses first, and inside them do the exponent: \(3^2 = 9\), so \((9 - 4) = 5\).

2. Now: \(6 + 2 \times 5\).

3. Multiplication before addition: \(2 \times 5 = 10\).

4. Addition: \(6 + 10 = 16\).

✅ Answer: 16

Tips

Always scan for brackets and powers before adding or multiplying.
Multiplication is not always before division — do whichever comes first reading left to right.
Rewrite the whole expression after each step so you don't lose track.