Order of Operations (BODMAS)
Learn the rules that tell you which part of a number sentence to calculate first. BODMAS makes sure everyone gets the same answer.
What is BODMAS?
BODMAS is a set of rules that tells us the order in which to do operations. Without these rules, different people could get different answers to the same problem!
B
Brackets
( ) first
O
Orders
Powers, square roots
D
Division
Left to right
M
Multiplication
Left to right
A
Addition
Left to right
S
Subtraction
Left to right
Important: Division and Multiplication have equal priority — do them left to right. The same applies to Addition and Subtraction.
Why Order Matters
Look at this problem: 3 + 4 × 2
Wrong (left to right)
3 + 4 = 7, then 7 × 2 = 14
Correct (BODMAS)
4 × 2 = 8 first, then 3 + 8 = 11
Using BODMAS, multiplication comes before addition, so the correct answer is 11.
Brackets Change Everything
Brackets tell you to do that part first, even if it would normally come later in BODMAS.
Compare:
Without brackets: 5 + 3 × 4
3 × 4 = 12 first
5 + 12 = 17
With brackets: (5 + 3) × 4
5 + 3 = 8 first (brackets!)
8 × 4 = 32
Multi-Step Problems
Example: (12 - 4) × 3 + 10 ÷ 2
Step 1 (B): (12 - 4) = 8. Now we have: 8 × 3 + 10 ÷ 2
Step 2 (DM): 8 × 3 = 24 and 10 ÷ 2 = 5. Now we have: 24 + 5
Step 3 (A): 24 + 5 = 29
Key Vocabulary
BODMAS
The rule for the order of operations: Brackets, Orders, Division, Multiplication, Addition, Subtraction.
Brackets
Symbols ( ) used to group parts of a calculation that must be done first.
Operation
A mathematical process: addition (+), subtraction (-), multiplication (×), or division (÷).
Expression
A number sentence that contains numbers and operations but no equals sign (e.g. 3 + 4 × 2).
Worked Examples
Calculate 20 - 3 × 4 + 1
Step 1 (M): 3 × 4 = 12. Now: 20 - 12 + 1
Step 2 (AS, left to right): 20 - 12 = 8, then 8 + 1 = 9
Answer: 9
Calculate (6 + 9) ÷ 3
Step 1 (B): 6 + 9 = 15
Step 2 (D): 15 ÷ 3 = 5
Calculate 2 × (15 - 7) + 18 ÷ 6
Step 1 (B): 15 - 7 = 8. Now: 2 × 8 + 18 ÷ 6
Step 2 (DM): 2 × 8 = 16 and 18 ÷ 6 = 3. Now: 16 + 3
Step 3 (A): 16 + 3 = 19
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is 8 + 2 × 5?
Question 2
What is (8 + 2) × 5?
Question 3
What is 30 - 12 ÷ 4 + 2?
Question 4
What does the B in BODMAS stand for?
Question 5
What is 4 × (3 + 7) - 20 ÷ 5?
Key Concepts Summary
- ●BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction.
- ●Always do Brackets first, then Orders, then Division/Multiplication, then Addition/Subtraction.
- ●Division and Multiplication have equal priority — work left to right.
- ●Addition and Subtraction have equal priority — work left to right.
- ●Brackets can override the normal order by grouping parts of a calculation.