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Order of Operations: Which Part of a Sum Do You Do First?

In one line: The order of operations is an agreed set of rules for which part of a calculation to do first: brackets, then powers, then multiplication and division from left to right, then addition and subtraction from left to right.

Why it works

A calculation like 2 + 3 × 4 could give 20 or 14 depending on what you do first, and maths only works if everyone gets the same answer. The order of operations is the shared rule that makes every calculation have one correct answer. An operation is just an action such as adding, subtracting, multiplying or dividing. You will need these rules for algebra, formulas in science, spreadsheets and calculators, so learning them well now saves a lot of confusion later. In the UK and Australia it is often remembered as BODMAS or BIDMAS (Brackets, Orders or Indices, Division and Multiplication, Addition and Subtraction). In the US it is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). A power, also called an index or exponent, is a small raised number that tells you how many times to multiply a number by itself, so 3² means 3 × 3.

Think of it like: Think of getting dressed in the morning. You must put on socks before shoes, and you must put on your shirt before your jumper. Some steps have to come first, or the result is a mess. Brackets are like a note saying 'do this bit first, no matter what'. Powers come next, then the 'stronger' steps of multiplying and dividing, and finally the 'lighter' steps of adding and subtracting. (Where this breaks: The analogy breaks in one important way: multiplication and division are equal partners, and so are addition and subtraction. Neither one in a pair always goes first. Instead you work through them from left to right, like reading a sentence. Getting dressed has no rule like that, so do not think of BODMAS as six separate steps in a strict line.)

Worked example

Work out 3 + 4 × (6 − 2)² ÷ 8

  1. Brackets first: 6 − 2 = 4, so the calculation becomes 3 + 4 × 4² ÷ 8.
  2. Powers next: 4² = 4 × 4 = 16, so it becomes 3 + 4 × 16 ÷ 8.
  3. Multiplication and division from left to right: 4 × 16 = 64, then 64 ÷ 8 = 8, so it becomes 3 + 8.
  4. Addition and subtraction last: 3 + 8 = 11.

Answer: 11

Common mistakes

  • Working straight from left to right (so 5 + 3 × 2 becomes 16); instead, do multiplication and division before addition and subtraction.
  • Always doing multiplication before division because M comes before D in PEMDAS (or D before M in BODMAS); instead, treat them as equals and work left to right.
  • Always doing addition before subtraction, so 10 − 3 + 2 becomes 5; instead, treat them as equals and work left to right to get 9.
  • Multiplying before working out a power, so 2 × 3² becomes 36; instead, do the power first: 3² = 9, then 2 × 9 = 18.

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Questions parents ask

What year do kids learn the order of operations?

In the UK it is formally taught in Year 6, and in Australia it is usually covered around Years 6–7. In the US, children start with brackets (parentheses) in grade 5 and add powers (exponents) in grade 6. It is then used constantly through secondary school algebra.

What is the difference between BODMAS, BIDMAS and PEMDAS?

They are the same rules with different names for the same steps. 'Orders', 'Indices' and 'Exponents' all mean powers, and 'Brackets' and 'Parentheses' mean the same thing. The only trap is that the letter order hides that multiplication and division are equal, and addition and subtraction are equal, so each pair is done left to right.

How can I help my child with the order of operations at home?

Ask your child to talk through each step out loud and rewrite the whole calculation after every step, as in the worked example above. Make up short sums with a 'trap', such as 10 − 4 + 2, and ask them to spot it before working it out. Checking answers together on a scientific calculator can also show them the rules in action.

Why do some calculators give a different answer?

Most scientific calculators and phone calculators follow the order of operations, but some very basic calculators work strictly left to right as you press each key. That is why 2 + 3 × 4 might show 20 on a simple calculator instead of the correct 14. Encourage your child to use brackets on the calculator when they are unsure.