Pro Mode Academy
Pro ModeAcademy
Login
MATHEMATICSNumber & Arithmetic
CURRENT TOPICBODMAS
(
)
²
● Master Topic Guide Verified 11+ Curriculum

BODMAS

Master Brackets, Orders, Division, Multiplication, Addition, Subtraction (BODMAS / BIDMAS) to solve multi-step calculations and word problems with confidence!

Practice Levels:Warm-UpCore ModePro Mode
Practice Papers
★ Master Topic Section11+ Essential Skill

📌 BODMAS / BIDMAS Rules

The order of operations tells us what to calculate first so everyone gets the exact same correct answer!

KEY IDEA

Without BODMAS, 3 + 4 × 2 could be 14 or 11. BODMAS proves the answer is 11!

THE ORDERB • O • D • M • A • S
B
BRACKETS( )
Do any calculations inside brackets first.
O
ORDERS / INDICESa², √x
Powers, square roots, and cube roots next.
D
DIVISION÷
Do divisions left to right.
M
MULTIPLICATION×
Do multiplications left to right.
A
ADDITION+
Do additions left to right.
S
SUBTRACTION−
Do subtractions left to right.
⭐ Left-to-Right Rule: When operations have equal priority (D & M, or A & S), solve left to right!
HOW TO USE BODMAS
  1. 1Look at the whole calculation.
  2. 2Do the operation that comes first in BODMAS.
  3. 3Same level operations? Work left to right.
  4. 4Continue step-by-step until complete.
EXAMPLE 124 ÷ 3 × (4 + 2) − 5
Step 1 BracketsDo brackets first: (4 + 2) = 6
24 ÷ 3 × 6 − 5
Step 2 DivisionDo division (left to right): 24 ÷ 3 = 8
8 × 6 − 5
Step 3 MultiplicationDo multiplication: 8 × 6 = 48
48 − 5
Step 4 SubtractionDo subtraction: 48 − 5
43
MORE EXAMPLESStep-by-step Solutions
EXAMPLE 218 − 3 × 2 + 10 ÷ 5
1. Mult & Div (L→R):
3 × 2 = 6, 10 ÷ 5 = 2
2. Expression becomes:
18 − 6 + 2
3. Add & Sub (L→R):
18 − 6 = 12 → 12 + 2
Answer = 14
EXAMPLE 32 × (3² + 4) − 6 ÷ 3
1. Orders inside Brackets:
3² = 9 → (9 + 4) = 13
2. Expression becomes:
2 × 13 − 6 ÷ 3
3. Mult & Div (L→R):
26 − 2
Answer = 24
EXAMPLE 4√81 + 4² × (10 − 3) ÷ 7
1. Brackets & Roots/Orders:
√81 = 9, 4² = 16, (10−3) = 7
2. Mult & Div (L→R):
16 × 7 ÷ 7 = 16
3. Addition:
9 + 16
Answer = 25
EXAMPLE 5100 ÷ 4 + 3 × 5 − 8 ÷ 2
1. Division (L→R):
100 ÷ 4 = 25, 8 ÷ 2 = 4
2. Multiplication:
3 × 5 = 15
3. Add & Sub (L→R):
25 + 15 − 4 = 36
Answer = 36
KEY NOTES
  • ★Brackets first, always!
  • ★Indices (or roots) next.
  • ★Division & Multiplication in order (left to right).
  • ★Addition & Subtraction in order (left to right).
  • ★BODMAS keeps the answer correct and avoids mistakes!
COMMON MISTAKES
❌ Doing addition before multiplication
Wrong: 2 + 3 × 4 = 20
Correct: 2 + 3 × 4 = 14
❌ Ignoring brackets
Wrong: 3 × (2 + 5) = 11
Correct: 3 × (2 + 5) = 21
❌ Not working left to right
Wrong: 20 ÷ 5 × 2 = 2
Correct: 20 ÷ 5 × 2 = 8
WHY IT MATTERS

BODMAS is used in everyday maths, across science subjects, and in real life! It ensures everyone gets the exact same correct answer.

⭐ TOP TIP: If you are ever unsure, write out B O D M A S on your paper and check off each letter!
★ Applied Exam Skills11+ Word Problems

📖 BODMAS Word Problems

Use BODMAS to solve multi-step real-world word problems step-by-step with complete confidence!

5 STEPS TO SUCCESS
1. READ → 2. UNDERSTAND → 3. PLAN → 4. SOLVE → 5. CHECK
STEPS TO SOLVE BODMAS WORD PROBLEMS
1READ

Read the problem carefully. Read it again if needed.

2UNDERSTAND

Identify key information and what is being asked.

3PLAN

Choose operations & order using BODMAS. Write expression.

4SOLVE

Carry out calculation following BODMAS. Show all working.

5CHECK

Does your answer make sense? Check your working.

EXAMPLE BODMAS WORD PROBLEMS11+ Exam Questions
1Pencil Packs

A shop sells 3 packs of pencils. Each pack has 12 pencils and costs £2.50. What is the total cost?

Plan: 3 × £2.50
Solve: 3 × £2.50 = £7.50
Answer: £7.50
2Flour Recipe

A recipe needs 4 cups of flour. Each cup weighs 125g. If I already have 350g of flour, how many more grams do I need?

Plan: (4 × 125) − 350
Solve: 500 − 350 = 150g
Answer: 150 g
3Concert Tickets

Tickets to a concert cost £18 each. A booking fee of £2.50 is added per ticket. I buy 6 tickets. How much do I pay in total?

Plan: 6 × (18 + 2.50)
Solve: 6 × 20.50 = £123.00
Answer: £123.00
4School Sports Club

A school has 240 students. 3/5 of the students are girls. Of the girls, 2/3 take part in a sports club. How many girls take part?

Plan: 240 × 3/5 × 2/3
Solve: 144 × 2/3 = 96
Answer: 96 girls
5Employee Bonus

A company gives each employee a bonus of £60. If there are 48 employees and the company's profit is increased by £1,200, what is the total new profit contribution?

Plan: (48 × 60) + 1,200
Solve: 2,880 + 1,200 = £4,080
Answer: £4,080
6Number Puzzle

A number when squared, then 3 is added, and the result is divided by 3 gives 13. What is the original number?

Plan: (x² + 3) ÷ 3 = 13
Solve: x² + 3 = 39 → x² = 36
Answer: x = 6
INTERACTIVE BODMAS QUIZ
3 + 4 × 5 =

Multiply first: 4 × 5 = 20, then 3 + 20

(12 − 4) × 3 =

Brackets first: 12 − 4 = 8, then 8 × 3

20 ÷ 4 + 2 × 6 =

Div & Mult: 20 ÷ 4 = 5, 2 × 6 = 12, then 5 + 12

2³ + 5 × 4 =

Indices: 2³ = 8, Mult: 5 × 4 = 20, then 8 + 20

30 − (2 + 3)² =

Brackets: 2 + 3 = 5, Index: 5² = 25, then 30 − 25

48 ÷ (3 + 3) × 2 =

Brackets: 3 + 3 = 6 → 48 ÷ 6 × 2 → Div/Mult L→R: 8 × 2 = 16

🚀 Ready to Test Your Knowledge?

Take our graded 11+ BODMAS assessment now!