Order of Operations (PEMDAS) Explained

When an expression mixes addition, multiplication, and brackets, the answer depends on the order you work in. Math uses one agreed order so everyone gets the same result. In the US it's taught as PEMDAS; elsewhere as BODMAS — they mean the same thing.

The order

1. Parentheses / Brackets — ( ) first.
2. Exponents / Orders — powers and roots.
3. Multiplication and Division — left to right (equal priority).
4. Addition and Subtraction — left to right (equal priority).

A worked example

Solve 3 + 6 × (5 + 4) ÷ 3 − 7:

1. Parentheses: 5 + 4 = 9 → 3 + 6 × 9 ÷ 3 − 7
2. Multiply/divide left to right: 6 × 9 = 54, then 54 ÷ 3 = 18 → 3 + 18 − 7
3. Add/subtract left to right: 3 + 18 = 21, then 21 − 7 = 14

The answer is 14.

The most common mistakes

• Doing addition before multiplication — the classic 3 + 6 × 2 is 15, not 18.
• Assuming M comes before D — multiplication and division are equal; work left to right.
• Forgetting left-to-right — 8 ÷ 2 × 4 is 16 (not 1), because you divide first, then multiply.

Let a calculator handle it

A good calculator applies these rules automatically. Our scientific calculatorrespects the order of operations, supports parentheses, exponents, and roots, and evaluates the whole expression at once — so you can type it as you'd write it. For percentage-specific problems, try the percentage calculator.

FAQ

Are PEMDAS and BODMAS different?

No — same rules, different names. BODMAS uses "Orders" for exponents and "Brackets" for parentheses.

Do multiplication and division really have the same priority?

Yes — you work through them left to right in the order they appear. The same goes for addition and subtraction.

What about a minus sign in front of a number?

That's a negative (unary minus). A scientific calculator handles it as part of the number it's attached to.