Simplification Using BODMAS

Class 5Operations (Grade 5)

BODMAS is a rule that tells us the correct order in which to perform operations in a mathematical expression. Without this rule, the same expression could give different answers depending on which operation you do first.

In Class 5, students learn to simplify expressions that involve two or more operations using the BODMAS rule. This ensures that everyone gets the same correct answer for the same expression.

What is Simplification Using BODMAS - Class 5 Maths (Operations)?

BODMAS stands for:

Letter	Operation	Symbol	Order
B	Brackets	( ), { }, [ ]	1st (innermost first)
O	Orders (powers, roots)	squared, cubed	2nd
D	Division	÷	3rd (left to right with M)
M	Multiplication	×	3rd (left to right with D)
A	Addition	+	4th (left to right with S)
S	Subtraction	−	4th (left to right with A)

Key rule: Division and Multiplication have the same priority — perform them left to right. Similarly, Addition and Subtraction have the same priority — perform them left to right.

Simplification Using BODMAS Formula

BODMAS: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right)

Solved Examples

Example 1: Example 1: Without brackets

Problem: Simplify: 8 + 4 × 3

Solution:

Step 1: Multiplication first: 4 × 3 = 12

Step 2: Then addition: 8 + 12 = 20

Answer: 20 (not 36, which you would get by adding first)

Example 2: Example 2: With brackets

Problem: Simplify: (8 + 4) × 3

Solution:

Step 1: Brackets first: 8 + 4 = 12

Step 2: Then multiplication: 12 × 3 = 36

Answer: 36

Example 3: Example 3: All four operations

Problem: Simplify: 18 + 12 ÷ 3 × 2 − 5

Solution:

Step 1: Division and Multiplication (left to right):

12 ÷ 3 = 4
4 × 2 = 8

Step 2: Addition and Subtraction (left to right):

18 + 8 = 26
26 − 5 = 21

Answer: 21

Example 4: Example 4: Nested brackets

Problem: Simplify: 50 − {20 + (8 − 3) × 2}

Solution:

Step 1: Innermost bracket first: (8 − 3) = 5

Step 2: Multiplication inside curly brackets: 5 × 2 = 10

Step 3: Addition inside curly brackets: 20 + 10 = 30

Step 4: Final subtraction: 50 − 30 = 20

Answer: 20

Example 5: Example 5: Division and multiplication from left to right

Problem: Simplify: 24 ÷ 6 × 2 ÷ 4

Solution:

Work left to right (D and M have equal priority):

Step 1: 24 ÷ 6 = 4

Step 2: 4 × 2 = 8

Step 3: 8 ÷ 4 = 2

Answer: 2

Example 6: Example 6: Word problem using BODMAS

Problem: Neha buys 3 notebooks at ₹45 each and 5 pens at ₹12 each. She pays with a ₹500 note. Express the change as a BODMAS expression and simplify.

Solution:

Change = 500 − (3 × 45 + 5 × 12)

Step 1: Inside brackets, do multiplications: 3 × 45 = 135 and 5 × 12 = 60

Step 2: Add inside brackets: 135 + 60 = 195

Step 3: Subtract: 500 − 195 = 305

Answer: Neha gets ₹305 as change.

Example 7: Example 7: Expression with orders (squares)

Problem: Simplify: 3 + 4² × 2

Solution:

Step 1: Orders first: 4² = 16

Step 2: Multiplication: 16 × 2 = 32

Step 3: Addition: 3 + 32 = 35

Answer: 35

Example 8: Example 8: Complex expression

Problem: Simplify: 100 − [30 + {5 × (12 − 8)}]

Solution:

Step 1: Innermost bracket: (12 − 8) = 4

Step 2: Multiplication in curly bracket: 5 × 4 = 20

Step 3: Addition in square bracket: 30 + 20 = 50

Step 4: Final subtraction: 100 − 50 = 50

Answer: 50

Example 9: Example 9: Real-life expression

Problem: Rahul scored (15 + 8) × 2 − 6 runs in a cricket game. How many runs did he score?

Solution:

Step 1: Brackets: 15 + 8 = 23

Step 2: Multiplication: 23 × 2 = 46

Step 3: Subtraction: 46 − 6 = 40

Answer: Rahul scored 40 runs.

Key Points to Remember

BODMAS = Brackets, Orders, Division, Multiplication, Addition, Subtraction.
Always solve brackets first, starting with the innermost bracket.
Division and Multiplication have equal priority — solve left to right.
Addition and Subtraction have equal priority — solve left to right.
Brackets override the normal order: (8 + 2) × 3 = 30, but 8 + 2 × 3 = 14.
Bracket types: ( ) round brackets → { } curly brackets → [ ] square brackets. Solve innermost first.
Without BODMAS, the same expression can give different wrong answers.

Practice Problems

Simplify: 15 − 3 × 4 + 2
Simplify: (15 − 3) × (4 + 2)
Simplify: 72 ÷ 8 + 4 × 3 − 1
Simplify: 100 − {40 − (15 + 5)}
Simplify: 5 × 6 + 8 ÷ 4 − 3
Dev had ₹200. He bought 4 pens at ₹15 each and 2 erasers at ₹5 each. Write a BODMAS expression for the remaining money and simplify.
Simplify: 36 ÷ (12 − 6) × 3 + 4
Simplify: [50 − {20 + (3 × 4)}] ÷ 2

Frequently Asked Questions

Q1. What does BODMAS stand for?

BODMAS stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction. It tells us the correct order to perform operations in a mathematical expression.

Q2. Why do we need BODMAS?

Without BODMAS, the same expression could give different answers. For example, 2 + 3 × 4 could be 20 (if you add first) or 14 (if you multiply first). BODMAS ensures everyone gets the same correct answer: 14.

Q3. Is BODMAS the same as PEMDAS?

Yes, they describe the same order. PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is used in the USA. BODMAS is used in India and the UK. Both give the same results.

Q4. Should I always do division before multiplication?

No. Division and multiplication have equal priority. Perform whichever comes first from left to right. In 12 × 3 ÷ 6, you multiply first (36 ÷ 6 = 6) because × appears before ÷ reading left to right.

Q5. What are the types of brackets and their order?

( ) round brackets are solved first, then { } curly brackets, then [ ] square brackets. Always solve the innermost bracket first and work outward.

Q6. How do I handle negative results inside brackets?

Perform the operation inside the brackets normally. If the result is negative, carry it forward. For example, in 10 + (3 − 8), the bracket gives −5, so the expression becomes 10 + (−5) = 5.

Q7. What does 'Orders' mean in BODMAS?

Orders refer to powers (exponents) and roots. For example, 3² = 9, √16 = 4. These are calculated after brackets but before the four basic operations. In Class 5, squares are the most common order.

Q8. Can brackets change the answer?

Yes. Brackets override the normal BODMAS order. For example: 2 + 3 × 4 = 14, but (2 + 3) × 4 = 20. The brackets force addition to happen before multiplication.

Simplification Using BODMAS

What is Simplification Using BODMAS - Class 5 Maths (Operations)?

Simplification Using BODMAS Formula

Solved Examples

Example 1: Example 1: Without brackets

Example 2: Example 2: With brackets

Example 3: Example 3: All four operations

Example 4: Example 4: Nested brackets

Example 5: Example 5: Division and multiplication from left to right

Example 6: Example 6: Word problem using BODMAS

Example 7: Example 7: Expression with orders (squares)

Example 8: Example 8: Complex expression

Example 9: Example 9: Real-life expression

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. What does BODMAS stand for?

Q2. Why do we need BODMAS?

Q3. Is BODMAS the same as PEMDAS?

Q4. Should I always do division before multiplication?

Q5. What are the types of brackets and their order?

Q6. How do I handle negative results inside brackets?

Q7. What does 'Orders' mean in BODMAS?

Q8. Can brackets change the answer?

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