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BODMAS tells you the order to work through a calculation. The letters stand for Brackets, Orders, Division, Multiplication, Addition and Subtraction. The acronym is useful, but it can also mislead you. This guide explains how to use it, where students lose marks and how to avoid those mistakes.
| Letter | Stands for | What it covers |
| B | Brackets | Anything inside ( ), [ ] or { }, starting with the innermost bracket |
| O | Orders | Powers, indices and roots, such as 3² or √16 |
| D | Division | ÷ |
| M | Multiplication | × |
| A | Addition | + |
| S | Subtraction | − |
You may also come across BIDMAS, where the I stands for Indices, and BEDMAS, where the E stands for Exponents. American textbooks use PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
All four describe the same rule. Different countries and textbooks simply use different words for the same ideas. Use whichever one your teacher uses.
The acronym hides one important rule.
Division and multiplication have equal priority. You do not do all the division first and then all the multiplication. You work from left to right and do whichever comes first.
Addition and subtraction also have equal priority. You work through them from left to right in the same way.
Because BODMAS lists D before M and A before S, it looks like a rule with six steps. In fact, it has four stages.
| Stage | What you do |
| 1 | Brackets, starting with the innermost bracket |
| 2 | Orders, which means powers, indices and roots |
| 3 | Division and multiplication, from left to right |
| 4 | Addition and subtraction, from left to right |
Here is the difference this rule makes.
| Work out 12 ÷ 3 × 2 Wrong. If you do all the division after the multiplication, you get 3 × 2 = 6, then 12 ÷ 6 = 2. Right. If you work from left to right, you get 12 ÷ 3 = 4, then 4 × 2 = 8. |
Both students used BODMAS. One got the wrong answer because they followed the order of the letters. Remember that stages 3 and 4 each work from left to right.
Start with the innermost bracket. If a bracket contains more than one operation, follow the full order of operations inside that bracket first.
A power applies only to the number it is attached to. In 2 × 3², the square applies only to the 3. This gives 2 × 9 = 18, not 6² = 36.
Do not do all the division first. Work through division and multiplication in the order they appear.
Do not do all the addition first. Work through addition and subtraction in the order they appear.
The same order applies when an expression includes algebra. Our beginner’s guide to Year 8 Maths explains how this works when you start expanding expressions.
Read your working back one line at a time. Most order of operations errors happen when you do the steps in the wrong order, not when you add or multiply incorrectly.
| Calculate 5 + 3 × 4 Multiply first. 3 × 4 = 12 Then add. 5 + 12 = 17 A common Year 7 mistake is to work from left to right without the rule. This gives 5 + 3 = 8, then 8 × 4 = 32, which is wrong. |
| Calculate 20 − 4 + 6 Addition and subtraction have equal priority, so work from left to right. 20 − 4 = 16 Then 16 + 6 = 22 If you add first, you get 4 + 6 = 10, then 20 − 10 = 10, which is wrong. |
| Calculate (6 + 2)² ÷ 4 Brackets first. 6 + 2 = 8 Then powers. 8² = 64 Then divide. 64 ÷ 4 = 16 |
| Calculate 3 × [10 − (2 + 3)] Innermost bracket first. 2 + 3 = 5 Then the outer bracket. 10 − 5 = 5 Then multiply. 3 × 5 = 15 |
| Calculate 2 + 18 ÷ 3² × 2 − 4 Powers first. 3² = 9, which gives 2 + 18 ÷ 9 × 2 − 4 Divide and multiply from left to right. 18 ÷ 9 = 2, then 2 × 2 = 4, which gives 2 + 4 − 4 Add and subtract from left to right. 2 + 4 = 6, then 6 − 4 = 2 |
Example 5 looks like a typical test question. The hardest part is working from left to right in stage 3.
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BODMAS does not mention these cases, but they come up often.
A fraction bar works like a bracket. Work out the whole top line (the numerator) and the whole bottom line (the denominator) separately. Then divide.
A minus sign in front of a power is not part of the power. −3² means −(3²), which equals −9. If you want to square negative three, write (−3)², which equals 9. Students lose many marks in algebra because of this rule.
A number next to a bracket means multiply. In 2(3 + 4), work out the bracket first. This gives 2 × 7 = 14.
| The mistake | What goes wrong | How to fix it |
| Doing all division before multiplication | 12 ÷ 3 × 2 is read as 12 ÷ 6 | Division and multiplication rank equally. Work from left to right. |
| Doing all addition before subtraction | 20 − 4 + 6 is read as 20 − 10 | Addition and subtraction rank equally. Work from left to right. |
| Applying a power to the wrong number | 2 × 3² is read as 6² | A power applies only to the number it is attached to. |
| Squaring a negative number without brackets | −3² is read as 9 | −3² equals −9. Write (−3)² if you mean 9. |
| Ignoring the fraction bar | The top and bottom lines get mixed together | Treat the fraction bar as brackets around the top and bottom lines. |
| Typing a long expression into a calculator | Calculators can read the same expression in different ways | Add your own brackets so the calculator reads it the way you mean. |
| Skipping lines of working | You cannot find the step where the mistake happened | Write one line of working for each stage. |
If you type the same expression into two different calculators, you can get two different answers. Adding brackets, even when you do not strictly need them, prevents this.
Students start using the order of operations in primary school. From Year 7 onwards, every Maths topic assumes you know it. The NSW Mathematics syllabus, published by NESA, builds Number and Algebra skills from primary school through to Year 12.
It pays to get this right early, because the same rule returns in algebra, index laws, substitution and later in calculus. Students who still make these mistakes in Year 9 Maths and Year 10 Maths often find the method is the problem, not the topic. Our beginner’s guide to Year 7 Maths shows where BODMAS fits among the other foundation topics.
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction. It tells you the order to work through a calculation. Orders means powers, indices and roots.
Both are correct, and they describe the same rule. Australia and the UK use BODMAS. The United States uses PEMDAS. Parentheses means brackets, and Exponents means orders.
No. Division and multiplication have equal priority. You work from left to right and do whichever comes first. In 12 ÷ 3 × 2, the answer is 8, not 2. Addition and subtraction work the same way.
Only the second letter changes. BODMAS uses Orders and BIDMAS uses Indices. Both mean powers and roots, so the rule is the same. Use whichever one your teacher uses.
Yes. A minus sign in front of a power is not part of the power. −3² equals −9, but (−3)² equals 9.
Treat the fraction bar as brackets around the top line and the bottom line. Work out each line separately, then divide.
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Written by Ruby
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