Concept 5 of 9
BODMAS: The Order Rule
Today's big idea
BODMAS fixes one order for every sum: brackets, orders, then ÷ and ×, then + and −.
Grabbing the signs left to right is the single commonest BODMAS mistake.
How it works
👀 What's going on?
Ask two friends for 4 + 5 × 2 and one may say 18 while the other says 14. One sum cannot have two answers.
💡 Here's the trick
Look at the ladder above. It fixes the order: brackets first, then orders, then division and multiplication, then addition and subtraction. So 4 + 5 × 2 turns into 4 + 10, which is 14.
🪄 How to do it
- 1.Start at the top of the ladder above with brackets, then powers.
- 2.Do division and multiplication next, moving left to right.
- 3.Do addition and subtraction last, moving left to right.
✍️ Try it
What is 20 − 3 × 6? Then: what is 7 × 3 + 40 ÷ 5?
In the first, 3 × 6 = 18, so 20 − 18 = 2. In the second, 7 × 3 = 21 and 40 ÷ 5 = 8, giving 29.
⚠️ Watch out
You might be thinking the six letters run strictly one at a time. Two pairs share a rung. Division and multiplication rank equal, and so do addition and subtraction, so those pairs go left to right.
🌟 Why this matters
Calculators, spreadsheets and shop tills all follow this same order. Key a sum in the wrong order and the total that comes back is wrong.
Exam tip: Underline the step you will do first before you write a single number down.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Solve: 12 + 3 × 4”
- 1
Read BODMAS order
B · O · D · M · A · S. Multiplication comes before addition. 📋
- 2
Spot the higher-priority op
The × beats +.
- 3
Multiply first
3 × 4 = 12
- 4
Then add ✓
12 + 12 = 24
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap each step in the right order — BODMAS tells you which operation comes first!
BODMAS ORDER · ROUND 1 OF 3
Order the BODMAS steps from first to last
Quick check
✅ VERIFICATION
What is the value of 30 + 8 ÷ 2?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Brackets
( ) → [ ] → { }, always solve the innermost first.