What does BODMAS stand for?

Brackets, Orders (powers and square roots), Division and Multiplication, Addition and Subtraction. BIDMAS (I for indices) and PEMDAS (used in the USA) are the same rules with different names.

Do you always divide before you multiply?

No. Division and multiplication have the same priority, so you do whichever comes first reading from left to right. 36 ÷ 4 × 3 is 9 × 3 = 27. Addition and subtraction work the same way: 18 − 6 + 2 is 12 + 2 = 14.

What is the answer to 6 ÷ 2(1 + 2)?

Using the order of operations as taught in Australian schools, it is 9: the bracket gives 3, then 6 ÷ 2 × 3 is worked from left to right, so 3 × 3 = 9. Some people and some calculators treat 2(1 + 2) as one block and get 1, which is why the question is badly written. In your own work, use extra brackets or a fraction so there is only one way to read it.

Is −3² equal to 9 or −9?

−9. The power applies only to the 3, and the minus sign is applied after it: −3² = −(3 × 3) = −9. To square negative 3, write (−3)², which is 9.

Does my calculator follow the order of operations?

A scientific calculator does: typing 3 + 4 × 2 gives 11. Many basic calculators work out each operation as you press it, so they give 14. When you use a basic calculator, work out the multiplication first yourself.

What year level learns the order of operations?

In the Victorian Curriculum 2.0, Year 6 works with brackets and combinations of operations. Year 7 uses all four operations with fractions and decimals, and Year 8 adds negative numbers. From then on it sits underneath every algebra topic, such as substitution and solving equations.

Order of Operations (BODMAS): Rules, Examples and Step-by-Step Checker

The order of operations rules

Work through a calculation in this order:

Step	What to do
1	Brackets, innermost first
2	Orders: powers and roots
3	Division and Multiplication, left to right
4	Addition and Subtraction, left to right

The letters D and M sit together because they have equal priority. So do A and S. That's the part most people forget: BODMAS does not mean division always comes before multiplication, or addition before subtraction.

You might also see BIDMAS (I for indices) or PEMDAS (parentheses, exponents). They're the same rules.

Multiplication before addition

Worked example

Work out $7 + 3 \times 5$ .

Multiplication comes before addition, even though the $+$ is written first.

7 + 3 \times 5

= 7 + 15

= 22

Going straight across gives $10 \times 5 = 50$ , which is wrong. A useful way to see it: $3 \times 5$ means "three fives", and you're adding $7$ to three fives.

Equal priority: work left to right

Worked example: division and multiplication

Work out $36 \div 4 \times 3$ .

Division and multiplication have equal priority, so go left to right. The division comes first.

36 \div 4 \times 3

= 9 \times 3

= 27

Worked example: subtraction and addition

Work out $18 - 6 + 2$ .

18 - 6 + 2

= 12 + 2

= 14

Doing the multiplication first would give $36 \div 12 = 3$ , and doing the addition first would give $18 - 8 = 10$ . Both are wrong. If it helps, think of subtracting $6$ as adding $-6$ : $18 + (-6) + 2 = 14$ , and now the order doesn't matter.

Brackets and powers

Worked example

Work out $5 \times (8 - 2)^2 \div 10$ .

5 \times (8 - 2)^2 \div 10

= 5 \times 6^2 \div 10 \qquad \text{(brackets)}

= 5 \times 36 \div 10 \qquad \text{(power)}

= 180 \div 10 \qquad \text{(left to right)}

= 18

Worked example: brackets inside brackets

Work out $50 - [3 \times (9 - 4) + 7]$ .

Start with the innermost brackets, then work outwards. Inside each bracket, the usual rules still apply.

50 - [3 \times (9 - 4) + 7]

= 50 - [3 \times 5 + 7]

= 50 - [15 + 7]

= 50 - 22

= 28

Square brackets $[\;]$ work exactly like round ones. They just make it easier to see which bracket closes where.

Order of operations checker (shows every step)

Type a calculation and it’s worked out one operation at a time, with the rule used at each step. Add your own answer to check it. Try one of the examples, or copy a question from your homework.

Negative numbers and powers

A power only applies to what's directly underneath it. In $-4^2$ the power belongs to the $4$ , and the minus sign is applied after:

-4^2 = -(4 \times 4) = -16

(-4)^2 = (-4) \times (-4) = 16

Worked example

Work out $10 - 2 \times (-3)^2$ .

10 - 2 \times (-3)^2

= 10 - 2 \times 9 \qquad \text{(power: } (-3)^2 = 9\text{)}

= 10 - 18

= -8

On a scientific calculator, type the brackets: $(-3)^2$ . Typing $-3$ then the $x^2$ key can give $-9$ on some calculators.

Fraction bars act like brackets

A fraction bar groups everything above it and everything below it. Work out the top and the bottom first, then divide.

Worked example

Work out $\dfrac{12 + 8}{9 - 4}$ .

\frac{12 + 8}{9 - 4} = \frac{20}{5} = 4

To type it into a calculator in one line, you need brackets: $(12 + 8) \div (9 - 4)$ . Typing $12 + 8 \div 9 - 4$ gives about $8.89$ , a different calculation.

The viral puzzles: 8 ÷ 2(2 + 2)

Puzzles like $8 \div 2(2 + 2)$ go round social media because people get two different answers. A number written next to a bracket means multiply, so this is $8 \div 2 \times (2 + 2)$ .

8 \div 2 \times (2 + 2)

= 8 \div 2 \times 4 \qquad \text{(brackets)}

= 4 \times 4 \qquad \text{(left to right)}

= 16

The other answer, $1$ , comes from treating $2(2 + 2)$ as a single block and doing it first. Using the rules taught in Australian schools, the answer is $16$ . But the real lesson is that the question is written badly. In your own working, write $\dfrac{8}{2} \times (2 + 2)$ or $\dfrac{8}{2(2 + 2)}$ , so only one answer is possible.

Common mistakes

Working straight across. $7 + 3 \times 5$ is not $50$ . Find the multiplication and division first: $7 + 15 = 22$ .
Multiplying before dividing every time. $36 \div 4 \times 3$ is not $3$ . Equal-priority operations go left to right, so it's $27$ .
Adding before subtracting every time. $18 - 6 + 2$ is not $10$ . Left to right gives $14$ .
Squaring the minus sign. $-4^2 = -16$ . Only $(-4)^2$ is $16$ .
Forgetting the brackets when typing a fraction. $\dfrac{12 + 8}{9 - 4}$ must be typed as $(12 + 8) \div (9 - 4)$ .
Rushing several steps at once. Write a new line after each operation. It's slower for one question and much faster than finding an error later.

Practice questions with answers

Work each one out without a calculator, then open the answer. If you get one wrong, put it into the checker above to see where your working went a different way.

$12 + 6 \div 3$
Show the answer
Divide first: $6 \div 3 = 2$ , then $12 + 2 = 14$ .
$9 - 4 + 2$
Show the answer
Left to right: $9 - 4 = 5$ , then $5 + 2 = 7$ .
$48 \div 6 \times 2$
Show the answer
Left to right: $48 \div 6 = 8$ , then $8 \times 2 = 16$ .
$(7 - 2) \times 4 + 1$
Show the answer
Brackets: $5$ . Then $5 \times 4 = 20$ , then $20 + 1 = 21$ .
$3 \times 2^3 - 5$
Show the answer
Power: $2^3 = 8$ . Then $3 \times 8 = 24$ , then $24 - 5 = 19$ .
$60 \div (4 + 2 \times 3)$
Show the answer
Inside the brackets, multiply first: $2 \times 3 = 6$ , so the bracket is $4 + 6 = 10$ . Then $60 \div 10 = 6$ .
$-5^2 + 3 \times (-2)$
Show the answer
Power first: $-5^2 = -25$ . Then $3 \times (-2) = -6$ . So $-25 + (-6) = -31$ .
$[4 + 2 \times (7 - 3)]^2 \div 8$
Show the answer
Inner brackets: $7 - 3 = 4$ . Square brackets: $4 + 2 \times 4 = 4 + 8 = 12$ . Power: $12^2 = 144$ . Then $144 \div 8 = 18$ .
$\dfrac{15 - 3}{2 \times 3}$
Show the answer
Work out the top and bottom separately: $\dfrac{12}{6} = 2$ .

The Tuterly Method

Snap. Fix. Ace.

Lost marks on a calculation? Snap it, find the step that went wrong, and fix it.

Snap.
Snap every question you get wrong, from tests, homework and class work.
Fix.
See the worked solution, then fresh questions on that skill. Even just one each day.
Ace.
A full practice test, with questions you've got wrong mixed in.

How the Tuterly Method works →

Order of operations by year level

Following the Victorian Curriculum 2.0. Schools sequence topics differently, so check your course.

Year 7

Fraction operations

All four operations with fractions and decimals, in the right order, with and without a calculator.

Worksheets and topic test · Free PDF with answers

Year 7

Expressions and the distributive law

Writing and evaluating expressions, where the order of operations decides what 2 + 3n means.

Worksheets and topic test · Free PDF with answers

Year 8

Integer operations

The order of operations with negative numbers, including powers of negatives.

Worksheets and topic test · Free PDF with answers

Year 7

Integers

Adding and subtracting negative numbers, the base skill for every calculation with signs.

Worksheets and topic test · Free PDF with answers

Order of operations (BODMAS)

The order of operations rules

Multiplication before addition

Equal priority: work left to right

Brackets and powers

Order of operations checker (shows every step)

Negative numbers and powers

Fraction bars act like brackets

The viral puzzles: 8 ÷ 2(2 + 2)

Common mistakes

Practice questions with answers

Order of operations by year level

Order of operations: common questions

More maths help, Years 7 to 10

Still losing marks on calculations?