Key takeaways
- BODMAS = Brackets, Orders, Division, Multiplication, Addition, Subtraction — the order you work through a calculation.
- Division and Multiplication rank equally: do them left to right, not D before M.
- Addition and Subtraction also rank equally and are done left to right.
- 3 + 4 × 2 = 11, not 14 — multiplication happens before addition.
- BIDMAS (I = Indices) and the US PEMDAS mean exactly the same thing.
BODMAS is the rule that tells you which part of a calculation to do first when a sum has more than one operation. Without it, 3 + 4 × 2 could be read two ways — and only one is correct. BODMAS makes sure every student (and every calculator) gets the same answer.
The letters stand for Brackets, Orders, Division, Multiplication, Addition, Subtraction. You work down the list from top to bottom. In the UK it's usually BODMAS; you'll also see BIDMAS (where I stands for Indices, another word for powers) and the American PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). All three describe the identical rule — the different words just reflect local vocabulary.
What each letter of BODMAS means
Here is what each step actually asks you to do, in order:
| Letter | Stands for | What you do |
|---|---|---|
| B | Brackets | Solve anything inside ( ), then [ ], then { } first. |
| O | Orders | Powers, indices and square roots — e.g. 2³ or √9. |
| D | Division | ÷ — done left to right with multiplication. |
| M | Multiplication | × — same rank as division. |
| A | Addition | + — done left to right with subtraction. |
| S | Subtraction | − — same rank as addition. |
The single idea students miss most: D and M are equal, and A and S are equal. BODMAS is really four levels, not six. When two operations sit at the same level, you simply work left to right.
How to solve a BODMAS problem, step by step
- 1
Deal with brackets first
Simplify everything inside brackets before you touch anything outside them. If there are nested brackets, work from the innermost outwards.
- 2
Handle orders (powers and roots)
Evaluate any indices or square roots next — for example, turn 2³ into 8 and √16 into 4.
- 3
Do division and multiplication, left to right
Scan the sum from left to right and carry out each × or ÷ as you reach it. Neither one automatically comes first.
- 4
Do addition and subtraction, left to right
Finally, work through the + and − signs from left to right to reach your answer.
Worked examples
Example 1 — multiplication before addition.
3 + 4 × 2
Do the multiplication first: 4 × 2 = 8. Then add: 3 + 8 = 11. The wrong answer, 14, comes from adding first.
Example 2 — brackets change everything.
(3 + 4) × 2
The bracket forces the addition first: 3 + 4 = 7, then 7 × 2 = 14. Same numbers as Example 1, different answer.
Example 3 — division and multiplication are equal.
20 ÷ 4 × 5
Go left to right: 20 ÷ 4 = 5, then 5 × 5 = 25. Doing the multiplication first (4 × 5 = 20, then 20 ÷ 20 = 1) is a classic error.
Example 4 — orders in the mix.
6 + 2² × 3
Orders first: 2² = 4. Then multiplication: 4 × 3 = 12. Then addition: 6 + 12 = 18.
Example 5 — addition and subtraction are equal.
10 − 3 + 2
Left to right: 10 − 3 = 7, then 7 + 2 = 9. Doing the addition first (3 + 2 = 5, then 10 − 5 = 5) is wrong.
Example 6 — brackets and orders together.
2 × (5 + 3²)
Inside the bracket, orders first: 3² = 9, then 5 + 9 = 14. Finally 2 × 14 = 28.
Example 7 — a longer chain.
8 + 12 ÷ 4 − 1
Division first: 12 ÷ 4 = 3. Now left to right: 8 + 3 = 11, then 11 − 1 = 10.
The mistakes students make most
"D always beats M"
Division does not outrank multiplication. They are equal — work left to right. 20 ÷ 4 × 5 = 25, not 1.
"S always beats A"
Subtraction does not come before addition. Same rank, left to right. 10 − 3 + 2 = 9, not 5.
Ignoring the power
Orders come straight after brackets. In 6 + 2² × 3, square the 2 before you multiply or add.
Skipping the brackets
Anything inside brackets is done first, even a whole sub-calculation. (3 + 4) × 2 = 14, not 11.
BODMAS vs BIDMAS vs PEMDAS
| BODMAS (UK/AU/NZ) | BIDMAS (UK) | PEMDAS (US) | |
|---|---|---|---|
| 1st | Brackets | Brackets | Parentheses |
| 2nd | Orders | Indices | Exponents |
| 3rd–4th (equal) | Division & Multiplication | Division & Multiplication | Multiplication & Division |
| 5th–6th (equal) | Addition & Subtraction | Addition & Subtraction | Addition & Subtraction |
| Same rule? | Yes | Yes | Yes |
Notice PEMDAS lists Multiplication before Division, while BODMAS lists division first. This is exactly why the left-to-right rule matters — the order the letters appear in the acronym is not a strict ranking for that middle pair. Teaching students the "equal levels, left to right" idea prevents almost every order-of-operations mistake, whichever acronym your curriculum uses.
Turn BODMAS into practice in seconds
Generate differentiated order-of-operations worksheets — with or without brackets and indices — and print a matching answer key.
Make BODMAS worksheets with AIFrequently asked questions
Brackets, Orders, Division, Multiplication, Addition, Subtraction. Orders means powers, indices and roots. You work through a calculation in that order, treating division/multiplication as one equal level and addition/subtraction as another.
Both are correct and mean the same thing. BIDMAS just uses 'Indices' instead of 'Orders' for powers and roots. The American version, PEMDAS, is identical too — only the words differ.
No. Division and multiplication have equal priority, so you do them left to right as they appear. For example, 20 ÷ 4 × 5 = 25, working left to right, not 1.
BODMAS says multiplication is done before addition, so 4 × 2 = 8 first, then 3 + 8 = 11. You'd only get 14 if you (incorrectly) added first, or if brackets grouped the 3 and 4 together.
Order of operations is usually introduced around Year 5–6 (ages 10–11) once students are confident with the four operations and brackets, then extended with indices in Year 7 and beyond.