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Order of Operations (PEMDAS)

Practise solving expressions in the right order — the PEMDAS rule that decides whether 3 + 4 × 2 is 11 or 14.

Grades 5–7 · 5.OA⚡ Foundational rule
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Why order matters & how PEMDAS works

When an expression mixes operations, you can’t just work left to right — the answer would change depending on where you started. Math fixes one agreed order so everyone gets the same result. The usual reminder is PEMDAS:

  1. Parentheses first.
  2. Exponents next.
  3. Multiplication and Division, left to right.
  4. Addition and Subtraction, left to right.

The key subtlety: multiply/divide rank equally (do them left to right), and so do add/subtract. PEMDAS is really four steps, not six.

Worked examples

Multiplication before addition3 + 4 × 2 — do 4 × 2 = 8 first, then 3 + 8 = 11 (not 14).
Parentheses first(3 + 4) × 2 — the brackets force 3 + 4 = 7 first, then 7 × 2 = 14.
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Tips & common mistakes

The single most common error is going strictly left to right and doing addition before multiplication. Train the habit of scanning the whole expression first: parentheses, then exponents, then any × or ÷, then + or −. The two worked examples above use the same numbers and get different answers — that’s the whole point of the rule.

  • Working left to right and ignoring precedence (3 + 4 × 2 is 11, not 14).
  • Thinking multiplication always comes before division — they’re equal, so go left to right.
  • Doing addition before subtraction by default — those are equal too.

Frequently asked questions

What does PEMDAS stand for?

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). It’s the agreed order for evaluating expressions.

Why do we need an order of operations?

So every person gets the same answer from the same expression. Without a fixed order, 3 + 4 × 2 could be 11 or 14.

Does multiplication always come before division?

No — they have equal priority, so you do them left to right. The same is true for addition and subtraction.

Is PEMDAS the same as BODMAS or BIDMAS?

Yes — they’re the same rule with different names. Brackets/parentheses and orders/exponents/indices mean the same thing.

What grade is order of operations?

It is introduced in grade 5 and used heavily through grades 6–7 and into algebra.

Keep practising

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