Order of Operations (PEMDAS) Explained Simply

If you've ever seen a viral math problem like 6 ÷ 2(1 + 2) spark a thousand arguments online, you've seen why the order of operations matters. It's the agreed set of rules that tells everyone — and every calculator — which part of an expression to evaluate first, so the same expression always gives the same answer.

What PEMDAS stands for

PEMDAS is a memory aid for the order:

• P — Parentheses (brackets)
• E — Exponents (powers and roots)
• MD — Multiplication and Division
• AS — Addition and Subtraction

You may know it as BODMAS or BIDMAS instead. They're identical rules — only the wording changes.

The one rule people forget

The most important nuance is hidden in the grouping. Multiplication and division are equal in priority, and you work through them left to right. The same goes for addition and subtraction.

That means in:

20 ÷ 5 × 2

you do the division first because it comes first reading left to right: 20 ÷ 5 = 4, then 4 × 2 = 8. You do not do the multiplication first to get 20 ÷ 10 = 2. Treating "MD" as "multiplication before division" is the single most common mistake.

Working through an example

Let's carefully evaluate:

3 + 4 × 2² − (6 − 1)

1. Parentheses first: (6 − 1) = 5. Now we have 3 + 4 × 2² − 5.
2. Exponents: 2² = 4. Now 3 + 4 × 4 − 5.
3. Multiplication/Division (left to right): 4 × 4 = 16. Now 3 + 16 − 5.
4. Addition/Subtraction (left to right): 3 + 16 = 19, then 19 − 5 = 14.

The answer is 14. You can check any expression like this with our scientific calculator, which follows PEMDAS automatically and can show the steps.

Why the viral problems are "ambiguous"

Expressions like 6 ÷ 2(1 + 2) cause fights because of an unwritten convention: some people read implied multiplication (the 2(…) part) as binding more tightly than division. Strict PEMDAS treats them as equal, giving 6 ÷ 2 × 3 = 9. The lesson isn't that one side is "wrong" — it's that good math uses parentheses to remove all doubt. Write (6 ÷ 2)(1 + 2) or 6 ÷ (2(1 + 2)) and nobody can misread it.

How this connects to algebra

Order of operations isn't just for arithmetic. When you solve an equation, you essentially undo operations in reverse PEMDAS order. To solve 2x + 3 = 11, you undo the addition first (2x = 8), then the multiplication (x = 4). Recognising the order an expression was built in tells you the order to take it apart — a skill you'll use constantly with tools like our quadratic equation calculator.

Quick checklist

Before you evaluate any expression, run through this:

1. Are there parentheses? Resolve the innermost first.
2. Any exponents or roots? Do those next.
3. Multiplication and division — left to right.
4. Addition and subtraction — left to right.

Follow those four steps and you'll get the right answer every time — and never lose an internet argument again.