Order of Operations (BODMAS)
When a maths expression has more than one operation (addition, subtraction, multiplication, division), the answer depends on the order in which you solve it. The BODMAS rule tells us the correct order so that everyone gets the same answer.
Without BODMAS, the expression 8 + 4 x 3 could be interpreted as (8 + 4) x 3 = 36 or 8 + (4 x 3) = 20. Using BODMAS, the correct answer is 20 because multiplication comes before addition.
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. This rule is universal — it is followed in every country and every branch of mathematics.
Mastering BODMAS in Class 5 prepares students for algebra, where expressions become longer and more complex. Every calculation involving mixed operations depends on this rule.
What is Order of Operations (BODMAS) - Class 5 Maths (Operations)?
BODMAS is a rule that defines the order in which operations must be performed in a mathematical expression.
| Letter | Stands For | Meaning | Priority |
|---|---|---|---|
| B | Brackets | Solve inside ( ), { }, [ ] first | 1st |
| O | Orders | Powers and roots (squares, cubes) | 2nd |
| D | Division | Divide (left to right) | 3rd |
| M | Multiplication | Multiply (left to right) | 3rd |
| A | Addition | Add (left to right) | 4th |
| S | Subtraction | Subtract (left to right) | 4th |
Important notes:
- Division and Multiplication have the same priority — solve from left to right.
- Addition and Subtraction have the same priority — solve from left to right.
- Always start with the innermost bracket first.
Order of Operations (BODMAS) Formula
BODMAS: Brackets → Orders → Division/Multiplication (L to R) → Addition/Subtraction (L to R)
Bracket hierarchy:
Innermost first: ( ) → { } → [ ]
Vinculum (bar): solve what is under the bar first
Types and Properties
Types of brackets:
- ( ) — Round brackets (parentheses) — solved first
- { } — Curly brackets (braces) — solved second
- [ ] — Square brackets — solved third
DMAS Rule (simplified BODMAS):
When there are no brackets or orders, use DMAS:
- D — Division (left to right)
- M — Multiplication (left to right)
- A — Addition (left to right)
- S — Subtraction (left to right)
Common mistake:
Students often solve from left to right without considering the priority. In 10 + 6 x 2, the answer is 22 (not 32), because multiplication is done before addition: 10 + 12 = 22.
Solved Examples
Example 1: Example 1: DMAS — No Brackets
Problem: Simplify: 12 + 8 x 3 - 4
Solution:
Step 1: Multiplication first: 8 x 3 = 24
Step 2: Expression becomes: 12 + 24 - 4
Step 3: Addition: 12 + 24 = 36
Step 4: Subtraction: 36 - 4 = 32
Answer: 32
Example 2: Example 2: With Brackets
Problem: Simplify: (15 + 5) x 4
Solution:
Step 1: Solve the bracket first: 15 + 5 = 20
Step 2: Multiply: 20 x 4 = 80
Answer: 80
Example 3: Example 3: Division and Multiplication (Left to Right)
Problem: Simplify: 48 / 6 x 2
Solution:
Step 1: Division and multiplication have the same priority. Go left to right.
Step 2: 48 / 6 = 8
Step 3: 8 x 2 = 16
Answer: 16
Example 4: Example 4: Nested Brackets
Problem: Simplify: [20 - {8 + (3 x 2)}]
Solution:
Step 1: Innermost bracket first: (3 x 2) = 6
Step 2: Expression becomes: [20 - {8 + 6}]
Step 3: Curly bracket: {8 + 6} = 14
Step 4: Square bracket: [20 - 14] = 6
Answer: 6
Example 5: Example 5: All Four Operations
Problem: Simplify: 36 / 4 + 5 x 3 - 7
Solution:
Step 1: Division: 36 / 4 = 9
Step 2: Multiplication: 5 x 3 = 15
Step 3: Expression becomes: 9 + 15 - 7
Step 4: Addition: 9 + 15 = 24
Step 5: Subtraction: 24 - 7 = 17
Answer: 17
Example 6: Example 6: Word Problem — Cricket Runs
Problem: In a cricket match, Arjun scored (25 + 15) runs in the first innings and 3 times that in the second innings. How many runs did he score in total?
Solution:
Step 1: First innings: (25 + 15) = 40 runs
Step 2: Second innings: 3 x 40 = 120 runs
Step 3: Total = 40 + 120 = 160 runs
As an expression: (25 + 15) + 3 x (25 + 15) = 40 + 120 = 160
Answer: Arjun scored 160 runs in total.
Example 7: Example 7: Word Problem — Shopping
Problem: Meera bought 4 notebooks at ₹35 each and 6 pens at ₹12 each. She paid with a ₹500 note. How much change did she get?
Solution:
Expression: 500 - (4 x 35 + 6 x 12)
Step 1: 4 x 35 = 140
Step 2: 6 x 12 = 72
Step 3: Bracket: 140 + 72 = 212
Step 4: 500 - 212 = 288
Answer: Meera got ₹288 as change.
Example 8: Example 8: Complex Expression with Nested Brackets
Problem: Simplify: 100 - [50 - {20 - (6 + 4)}]
Solution:
Step 1: Innermost bracket: (6 + 4) = 10
Step 2: Curly bracket: {20 - 10} = 10
Step 3: Square bracket: [50 - 10] = 40
Step 4: Final: 100 - 40 = 60
Answer: 60
Example 9: Example 9: Multiple Operations
Problem: Simplify: 5 x 6 + 72 / 8 - 3 x 4
Solution:
Step 1: Multiplication: 5 x 6 = 30
Step 2: Division: 72 / 8 = 9
Step 3: Multiplication: 3 x 4 = 12
Step 4: Expression becomes: 30 + 9 - 12
Step 5: Left to right: 30 + 9 = 39, then 39 - 12 = 27
Answer: 27
Example 10: Example 10: Brackets Changing the Answer
Problem: Show that brackets change the answer: Calculate 24 - 8 / 4 and (24 - 8) / 4.
Solution:
Without extra brackets: 24 - 8 / 4
Step 1: Division first: 8 / 4 = 2
Step 2: 24 - 2 = 22
With brackets: (24 - 8) / 4
Step 1: Bracket first: 24 - 8 = 16
Step 2: 16 / 4 = 4
Answer: 24 - 8 / 4 = 22, but (24 - 8) / 4 = 4. Brackets change the order and the result.
Real-World Applications
Where BODMAS is used in daily life:
- Shopping bills: Calculating total cost when buying different items in different quantities: 3 x ₹45 + 5 x ₹20. Using BODMAS: multiply first (₹135 + ₹100), then add = ₹235.
- Cooking: Scaling a recipe that uses mixed operations. If a recipe needs (2 x 100) + 50 grams of flour, BODMAS gives 200 + 50 = 250 g.
- Score calculation: In a quiz, total score = right answers x marks per question - wrong answers x penalty. For 12 right (3 marks each) and 4 wrong (1 mark penalty): 12 x 3 - 4 x 1 = 36 - 4 = 32.
- Budgeting: Monthly savings = Income - (Rent + Food + Transport). The bracket ensures all expenses are totalled before subtracting.
- Science: Every physics formula (speed = distance/time, force = mass x acceleration) relies on BODMAS for correct evaluation.
- Spreadsheets and calculators: Computers follow BODMAS exactly. If you type 2 + 3 * 4 into a spreadsheet, it returns 14 (not 20).
Step-by-step approach for complex expressions:
- Copy the expression.
- Solve brackets first. Underline or circle the bracket portion.
- Handle division and multiplication (left to right). Rewrite the expression after each step.
- Handle addition and subtraction (left to right).
- Write the final answer.
Rewriting after each step helps avoid mistakes. Do not try to do multiple steps in your head at once.
Key Points to Remember
- BODMAS = Brackets, Orders, Division, Multiplication, Addition, Subtraction.
- Division and Multiplication have equal priority — solve left to right.
- Addition and Subtraction have equal priority — solve left to right.
- Always solve the innermost bracket first: ( ) → { } → [ ].
- Brackets can change the answer: 5 + 3 x 2 = 11, but (5 + 3) x 2 = 16.
- When there are no brackets or orders, use the simplified DMAS rule.
- BODMAS is also called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) in some countries.
Practice Problems
- Simplify: 15 + 6 x 4 - 10
- Simplify: (18 + 12) / 5 x 3
- Simplify: 100 - 48 / 8 + 7 x 3
- Simplify: [36 - {14 + (3 x 2)}]
- Ria buys 5 books at ₹65 each and 3 pens at ₹15 each. She gets a discount of ₹50. Express and solve using BODMAS.
- Simplify: 8 x 9 - 56 / 7 + 12
- Simplify: 200 - [100 - {50 - (10 + 5)}]
- Place brackets to make this true: 6 + 2 x 5 = 40
Frequently Asked Questions
Q1. What is BODMAS?
BODMAS is a rule that gives the order in which mathematical operations must be performed: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. It ensures everyone gets the same answer for the same expression.
Q2. What is the difference between BODMAS and DMAS?
DMAS is a simplified version of BODMAS used when there are no brackets or orders (powers). DMAS stands for Division, Multiplication, Addition, Subtraction. BODMAS includes brackets and orders as well.
Q3. Do we always do division before multiplication?
No. Division and multiplication have the same priority. When both appear in an expression, solve from left to right. In 12 x 3 / 6, first multiply: 36 / 6 = 6. In 12 / 3 x 6, first divide: 4 x 6 = 24.
Q4. What happens if there are nested brackets?
Solve the innermost bracket first. Work outward: round brackets ( ) first, then curly brackets { }, then square brackets [ ]. For example, in [20 - {5 + (2 x 3)}], solve (2 x 3) = 6 first, then {5 + 6} = 11, then [20 - 11] = 9.
Q5. Why do brackets change the answer?
Brackets override the normal order of operations by forcing the expression inside them to be solved first. In 2 + 3 x 4, BODMAS gives 14. But in (2 + 3) x 4, the bracket makes addition happen first, giving 20.
Q6. Is BODMAS the same as PEMDAS?
Yes, they describe the same rule. PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is used in the USA. BODMAS is used in India and the UK. The order of operations is identical.
Q7. What does the 'O' in BODMAS stand for?
O stands for Orders, which means powers (exponents) and roots. For example, in 3 + 2 squared, you calculate 2 squared = 4 first, then add 3 to get 7. In Class 5, orders are introduced but used sparingly.
Q8. How do you solve addition and subtraction in BODMAS?
Addition and subtraction have the same priority. Solve them from left to right. In 20 - 5 + 3, first subtract: 15, then add: 18. Do not add first just because A comes before S in BODMAS.
Q9. Can BODMAS be used for word problems?
Yes. First convert the word problem into a mathematical expression, then apply BODMAS. For example, if Kavi buys 3 pens at ₹10 each and 2 notebooks at ₹25 each, the total is 3 x 10 + 2 x 25. Multiply first, then add: 30 + 50 = ₹80.
Q10. What is a common mistake students make with BODMAS?
The most common mistake is solving from left to right without considering priority. In 5 + 2 x 6, students often add first to get 42, but the correct answer is 5 + 12 = 17 because multiplication comes before addition.
Related Topics
- Addition of Large Numbers
- Multiplication of Large Numbers
- Subtraction of Large Numbers
- Division of Large Numbers
- Word Problems on Four Operations
- Mental Math (Grade 5)
- Multiplication of 4-Digit Numbers
- Division of 4-Digit by 2-Digit Numbers
- Simplification Using BODMAS
- Properties of Operations (Grade 5)
- Unitary Method (Grade 5)
- Mixed Word Problems (Grade 5)
