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PEMDAS: The Order of Operations

In one line: PEMDAS is a memory aid for the order in which you work out a calculation: Parentheses (brackets) first, then Exponents (powers), then Multiplication and Division from left to right, then Addition and Subtraction from left to right.

Why it works

A calculation like 3 + 4 × 2 could give 14 or 11 depending on which part you do first. Mathematicians agree on one order so that everyone gets the same answer. Without that agreement, calculators, spreadsheets and people would all disagree. Knowing PEMDAS is also the foundation for algebra, where you will simplify longer expressions with letters in them.

Think of it like: Think of getting dressed in the morning. You put on socks before shoes, and a shirt before a jumper, or things go wrong. PEMDAS is like a getting-dressed checklist for a calculation: deal with the brackets first, then the powers, then multiply and divide, and finally add and subtract. (Where this breaks: Getting dressed has a fixed order because of how clothes work, but PEMDAS is a rule people agreed on. Also, PEMDAS has two 'tied' pairs: multiplication and division have equal rank, and so do addition and subtraction. For each tied pair, you simply work from left to right, rather than always doing M before D or A before S.)

Worked example

Work out 8 + 2 × (6 − 3)² ÷ 6

  1. Parentheses first: 6 − 3 = 3, so the calculation becomes 8 + 2 × 3² ÷ 6.
  2. Exponents next: an exponent tells you how many times to multiply a number by itself, so 3² = 3 × 3 = 9. Now it is 8 + 2 × 9 ÷ 6.
  3. Multiplication and division, left to right: 2 × 9 = 18, then 18 ÷ 6 = 3. Now it is 8 + 3.
  4. Addition and subtraction, left to right: 8 + 3 = 11.

Answer: 11

Common mistakes

  • Doing multiplication before division every time because M comes before D in the word; instead, treat them as equal and work from left to right.
  • Doing addition before subtraction every time because A comes before S; instead, treat them as equal and work from left to right.
  • Simply working from left to right through the whole calculation, such as doing 3 + 4 before × 2; instead, always check for brackets, powers, multiplication and division first.
  • Reading 3² as 3 × 2 = 6; instead, remember an exponent means multiplying the number by itself, so 3² = 3 × 3 = 9.

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Questions parents ask

What grade do kids learn PEMDAS?

In the US, children usually start using parentheses in grade 5 and add exponents in grade 6, with lots of practice in grade 7. In the UK, the order of operations is taught in Year 6, and in Australia it appears around Years 6 and 7.

Is PEMDAS the same as BODMAS or BIDMAS?

Yes, they describe the same rules with different words. In the UK and Australia, children often learn BODMAS or BIDMAS, where B stands for Brackets and O or I stands for Orders or Indices, which are other names for exponents.

Why does my child get the wrong answer even when following PEMDAS?

The most common reason is doing all multiplication before any division, or all addition before any subtraction, because of the order of letters in the word. Remind your child that each of these pairs is equal in rank and is worked from left to right.

How can I help my child with PEMDAS at home?

Write a short calculation and ask your child to explain each step out loud, underlining the part they will do next. You can also invent a calculation, have them predict the answer, and then check it together on a scientific calculator, which follows the same order.