Simplification: Formulas, Concepts, Tricks & Step-by-Step Rules for BODMAS

Q: Why is BODMAS important in simplification?

It ensures every operation is performed in the correct sequence so the final answer is accurate.

Q: Why must brackets be solved first?

Brackets enclose expressions that must be completed before combining with the rest of the operations.

Q: What is the correct order of bracket removal?

Always remove in sequence: ( ) → { } → \[ \].

Q: Why is “of” solved before division and multiplication?

Because “of” always represents direct multiplication and has higher priority.

Q: What is the meaning of modulus in simplification?

Modulus gives the absolute value of a number, always producing a positive result.

Q: Why does vinculum come before BODMAS operations?

Vinculum groups values at the highest priority and must be solved before brackets.

Q: Are division and multiplication equal in priority?

Yes, both are solved left to right based on their appearance in the expression.

Q: When should addition and subtraction be performed?

Only after completing brackets, of, division, and multiplication.

Q: Why do students frequently make mistakes in simplification?

Because they follow left-to-right blindly without respecting operation priority.

Q: What is the simplest way to master BODMAS?

Practise expressions regularly while strictly following the order: Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction.

Simplification is one of the most scoring and logic-driven topics in quantitative aptitude. Yet many students get confused because expressions often include brackets, operators, modulus, and vinculum, all layered in different orders. These layers change how values combine, and even a small deviation in applying the rules leads to incorrect answers.

If you understand these three ideas clearly:
✔ Order of operations
✔ Priority of brackets and symbols
✔ How special terms like modulus & vinculum work

Then you can solve ANY simplification question quickly and accurately.

This Simplification using BODMAS Rule guide covers all formulas, concepts, shortcuts, cases, examples, FAQs, and exam tips, making it the perfect one-stop resource for SSC, Banking, Railways, State Exams, and campus aptitude tests.

Quick Overview: Simplification (BODMAS, Modulus, Vinculum) Formulas

Concept / Situation	Considered	Used	Formula (With Meaning of Symbols Inside Row)
Order of Operations (BODMAS)	Priority of operations	Apply step-by-step	V → B → O → D → M → A → S (V = Vinculum, B = Brackets, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)
Bracket Removal Rule	Bracket type order	Solve inside-out	( ) → { } → [ ] (Solve innermost first)
“of” Operation	Fraction/percentage application	Convert to multiplication	a of b = a × b (Used for %, fractions, ratios)
Division Operation	Equal priority with multiplication	Left → Right	a ÷ b meaning a divided by b
Multiplication Operation	After division (if appearing later)	Left → Right	a × b multiply values
Addition Operation	Only after × and ÷ finish	Left → Right	a + b combine values
Subtraction Operation	Lowest priority	Solve last	a − b subtract values
Modulus of a number	Sign removal	Always positive	(
Vinculum (Bar)	Highest priority component	Solve before BODMAS	a+b−c‾\overline{a+b-c}a+b−c solve bar expression first

Formulas for Simplification (BODMAS, Modulus, Vinculum)

1. BODMAS Formula

BODMAS is the foundation of all simplification problems. It tells you which operation must be done first and which must be done last.

Formula (Order of Operations):

Vinculum→Brackets→Of→Division→Multiplication→Addition→Subtraction

Why this formula works

Each operation changes the value differently.
If you change the order, the final value becomes incorrect.

Example pattern:

Multiplication before addition
Division before multiplication
Of before division
Brackets before everything

Common mistakes

Doing left-to-right without priority
Adding/subtracting too early
Ignoring "of"
Solving brackets in the wrong order

2. Bracket Removal Formula

Correct Order:

()→{}→[]

Why this formula works

Brackets are layers, and the innermost must be solved first to avoid incorrect sequencing.

Example

8+[5−{3−(2−1)}]

Step-by-step:

Solve ( ) → (2 − 1) = 1
Solve { } → 3 − 1 = 2
Solve [ ] → 5 − 2 = 3
Final → 8+3=11

3. “of” Formula (Convert to Multiplication)

Formula:

a of b = a×b

Why this formula works

In mathematics, “of” simply means multiplication:

Fractions
Percentages
Ratios

Example:

1/4 of 80 = (¼)×80 = 20

4. Division Formula

Formula:

a÷b = a/b

Important Rule:

Division and multiplication have equal priority
→ Solve from left to right.

Example

48÷4×2 = (48÷4)×2 = 12×2 = 24

5. Multiplication Formula

Formula:

a×b

When to use

After:

Vinculum
Brackets
Of
Division (if division appears before multiplication)

Example

6+3×4 = 6+12 = 18

6. Addition & Subtraction Formula

Formulas:

a+b and a−b

Rule

Use only after all other operations are done.

Example

20−5+4 = (20−5)+4 = 15+4 = 19

7. Modulus Formula

Formula:

∣a∣ = {a if a>0

{−a if a<0

Explanation

Modulus removes the sign and converts the value to positive.

Example:

∣−7+2∣ = ∣−5∣ = 5

8. Vinculum Formula (Highest Priority)

Formula:

a+b−c‾

Explanation

Everything under the bar must be solved first, even before brackets.

Example

10−6−2+1‾

Solve under bar:

6−2+1 = 5

Now full:

10−5 = 5

Smart Tips and Practical Tricks for Solving Simplification (BODMAS) Problems

Mastering Simplification becomes easy when you clearly understand how each operation works, how brackets change the expression, and how symbols like modulus and vinculum influence the order. Most students make mistakes not because the formulas are hard, but because they do not follow the correct operation sequence.
This section breaks down the most important ideas into clear, actionable tips so you can solve expressions faster, more accurately, and with complete confidence.

1. Always Identify and Solve the Highest-Priority Operation First

Every simplification question contains multiple operations: brackets, of, division, multiplication, addition, subtraction.
The priority is ALWAYS:

Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction

Even one wrong step changes the entire answer.
Following the sequence eliminates the majority of mistakes.

2. Remove Brackets in the Correct Order

Many expressions contain three types of brackets:

✔ Parentheses ( )
✔ Curly braces { }
✔ Square brackets [ ]

They must be removed in this exact order:

( ) → { } → [ ]

Solving the innermost bracket first keeps the expression clean and prevents conceptual errors.

3. Convert “of” into Multiplication Immediately

Words like “of” in maths ALWAYS mean multiplication.

Examples:
½ of 60 = ½ × 60
25% of 240 = 25/100 × 240

This one conversion makes the rest of the operations straightforward.

4. Solve Vinculum Before Applying BODMAS

A vinculum (bar drawn over numbers) behaves like the highest priority bracket.

Example:

12+6−2+1‾

Solve the expression under the bar first.
Ignoring vinculum is one of the most common reasons students get wrong answers.

5. Handle Modulus Carefully - It Always Produces a Positive Value

Modulus changes negative values into positive ones.

∣−9∣ = 9
∣7−12∣ = ∣−5∣ = 5

Whenever absolute value is present, simplify inside first, then make it positive.

6. Perform Division and Multiplication from Left to Right

Many students know the priority but still make this mistake:

Division does NOT always come before multiplication.
They are equal in rank and must be solved left to right.

Example:
48 ÷ 4 × 2
Solve as (48 ÷ 4) × 2 = 12 × 2 = 24

If you reverse the order, the answer becomes wrong.

7. Do Not Add or Subtract Until All Higher Operations Are Over

Addition and subtraction must be performed only after simplifying:

✔ brackets
✔ of
✔ division
✔ multiplication

Rushing into addition/subtraction is one of the biggest exam errors.

8. Write a Clean Step-by-Step Breakdown

During exams, messy steps cause confusion.

Always simplify neatly:

Write one step per operation
Avoid skipping steps
Avoid doing mental operations when expression is long

This keeps your calculation error-free.

9. Recognize Common Expression Patterns

Most problems repeat the same structures:

✔ Nested brackets
✔ Mixed operations
✔ Modulus + bracket
✔ Vinculum + inner expression
✔ Percentage / fraction with “of”

Identifying patterns gives instant clarity and reduces solving time dramatically.

10. Practice Exam-Type Expressions Frequently

Simplification appears in:

SSC (CGL, CHSL, GD)
Banking (IBPS, SBI)
Railway RRB
State PSC
Defence exams
Campus aptitude tests

The more you practise, the faster your mind automatically follows the operation hierarchy, leading to near-instant solutions.

FAQs About Simplification, BODMAS, Modulus & Vinculum

Q1. Why is BODMAS important in simplification?

It ensures every operation is performed in the correct sequence so the final answer is accurate.

Q2. Why must brackets be solved first?

Brackets enclose expressions that must be completed before combining with the rest of the operations.

Q3. What is the correct order of bracket removal?

Always remove in sequence: ( ) → { } → [ ].

Q4. Why is “of” solved before division and multiplication?

Because “of” always represents direct multiplication and has higher priority.

Q5. What is the meaning of modulus in simplification?

Modulus gives the absolute value of a number, always producing a positive result.

Q6. Why does vinculum come before BODMAS operations?

Vinculum groups values at the highest priority and must be solved before brackets.

Q7. Are division and multiplication equal in priority?

Yes, both are solved left to right based on their appearance in the expression.

Q8. When should addition and subtraction be performed?

Only after completing brackets, of, division, and multiplication.

Q9. Why do students frequently make mistakes in simplification?

Because they follow left-to-right blindly without respecting operation priority.

Q10. What is the simplest way to master BODMAS?

Practise expressions regularly while strictly following the order: Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction.

Aptitude

Simplification: Formulas, Concepts, Tricks & Step-by-Step Rules for BODMAS

If you understand these three ideas clearly:
✔ Order of operations
✔ Priority of brackets and symbols
✔ How special terms like modulus & vinculum work

Then you can solve ANY simplification question quickly and accurately.

Quick Overview: Simplification (BODMAS, Modulus, Vinculum) Formulas

Concept / Situation	Considered	Used	Formula (With Meaning of Symbols Inside Row)
Order of Operations (BODMAS)	Priority of operations	Apply step-by-step	V → B → O → D → M → A → S (V = Vinculum, B = Brackets, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)
Bracket Removal Rule	Bracket type order	Solve inside-out	( ) → { } → [ ] (Solve innermost first)
“of” Operation	Fraction/percentage application	Convert to multiplication	a of b = a × b (Used for %, fractions, ratios)
Division Operation	Equal priority with multiplication	Left → Right	a ÷ b meaning a divided by b
Multiplication Operation	After division (if appearing later)	Left → Right	a × b multiply values
Addition Operation	Only after × and ÷ finish	Left → Right	a + b combine values
Subtraction Operation	Lowest priority	Solve last	a − b subtract values
Modulus of a number	Sign removal	Always positive	(
Vinculum (Bar)	Highest priority component	Solve before BODMAS	a+b−c‾\overline{a+b-c}a+b−c solve bar expression first

Formulas for Simplification (BODMAS, Modulus, Vinculum)

1. BODMAS Formula

BODMAS is the foundation of all simplification problems. It tells you which operation must be done first and which must be done last.

Formula (Order of Operations):

Vinculum→Brackets→Of→Division→Multiplication→Addition→Subtraction

Why this formula works

Each operation changes the value differently.
If you change the order, the final value becomes incorrect.

Example pattern:

Multiplication before addition
Division before multiplication
Of before division
Brackets before everything

Common mistakes

Doing left-to-right without priority
Adding/subtracting too early
Ignoring "of"
Solving brackets in the wrong order

2. Bracket Removal Formula

Correct Order:

()→{}→[]

Why this formula works

Brackets are layers, and the innermost must be solved first to avoid incorrect sequencing.

Example

8+[5−{3−(2−1)}]

Step-by-step:

Solve ( ) → (2 − 1) = 1
Solve { } → 3 − 1 = 2
Solve [ ] → 5 − 2 = 3
Final → 8+3=11

3. “of” Formula (Convert to Multiplication)

Formula:

a of b = a×b

Why this formula works

In mathematics, “of” simply means multiplication:

Fractions
Percentages
Ratios

Example:

1/4 of 80 = (¼)×80 = 20

4. Division Formula

Formula:

a÷b = a/b

Important Rule:

Division and multiplication have equal priority
→ Solve from left to right.

Example

48÷4×2 = (48÷4)×2 = 12×2 = 24

5. Multiplication Formula

Formula:

a×b

When to use

After:

Vinculum
Brackets
Of
Division (if division appears before multiplication)

Example

6+3×4 = 6+12 = 18

6. Addition & Subtraction Formula

Formulas:

a+b and a−b

Rule

Use only after all other operations are done.

Example

20−5+4 = (20−5)+4 = 15+4 = 19

7. Modulus Formula

Formula:

∣a∣ = {a if a>0

{−a if a<0

Explanation

Modulus removes the sign and converts the value to positive.

Example:

∣−7+2∣ = ∣−5∣ = 5

8. Vinculum Formula (Highest Priority)

Formula:

a+b−c‾

Explanation

Everything under the bar must be solved first, even before brackets.

Example

10−6−2+1‾

Solve under bar:

6−2+1 = 5

Now full:

10−5 = 5

Smart Tips and Practical Tricks for Solving Simplification (BODMAS) Problems

1. Always Identify and Solve the Highest-Priority Operation First

Every simplification question contains multiple operations: brackets, of, division, multiplication, addition, subtraction.
The priority is ALWAYS:

Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction

Even one wrong step changes the entire answer.
Following the sequence eliminates the majority of mistakes.

2. Remove Brackets in the Correct Order

Many expressions contain three types of brackets:

✔ Parentheses ( )
✔ Curly braces { }
✔ Square brackets [ ]

They must be removed in this exact order:

( ) → { } → [ ]

Solving the innermost bracket first keeps the expression clean and prevents conceptual errors.

3. Convert “of” into Multiplication Immediately

Words like “of” in maths ALWAYS mean multiplication.

Examples:
½ of 60 = ½ × 60
25% of 240 = 25/100 × 240

This one conversion makes the rest of the operations straightforward.

4. Solve Vinculum Before Applying BODMAS

A vinculum (bar drawn over numbers) behaves like the highest priority bracket.

Example:

12+6−2+1‾

Solve the expression under the bar first.
Ignoring vinculum is one of the most common reasons students get wrong answers.

5. Handle Modulus Carefully - It Always Produces a Positive Value

Modulus changes negative values into positive ones.

∣−9∣ = 9
∣7−12∣ = ∣−5∣ = 5

Whenever absolute value is present, simplify inside first, then make it positive.

6. Perform Division and Multiplication from Left to Right

Many students know the priority but still make this mistake:

Division does NOT always come before multiplication.
They are equal in rank and must be solved left to right.

Example:
48 ÷ 4 × 2
Solve as (48 ÷ 4) × 2 = 12 × 2 = 24

If you reverse the order, the answer becomes wrong.

7. Do Not Add or Subtract Until All Higher Operations Are Over

Addition and subtraction must be performed only after simplifying:

✔ brackets
✔ of
✔ division
✔ multiplication

Rushing into addition/subtraction is one of the biggest exam errors.

8. Write a Clean Step-by-Step Breakdown

During exams, messy steps cause confusion.

Always simplify neatly:

Write one step per operation
Avoid skipping steps
Avoid doing mental operations when expression is long

This keeps your calculation error-free.

9. Recognize Common Expression Patterns

Most problems repeat the same structures:

✔ Nested brackets
✔ Mixed operations
✔ Modulus + bracket
✔ Vinculum + inner expression
✔ Percentage / fraction with “of”

Identifying patterns gives instant clarity and reduces solving time dramatically.

10. Practice Exam-Type Expressions Frequently

Simplification appears in:

SSC (CGL, CHSL, GD)
Banking (IBPS, SBI)
Railway RRB
State PSC
Defence exams
Campus aptitude tests

The more you practise, the faster your mind automatically follows the operation hierarchy, leading to near-instant solutions.

FAQs About Simplification, BODMAS, Modulus & Vinculum

Q1. Why is BODMAS important in simplification?

It ensures every operation is performed in the correct sequence so the final answer is accurate.

Q2. Why must brackets be solved first?

Brackets enclose expressions that must be completed before combining with the rest of the operations.

Q3. What is the correct order of bracket removal?

Always remove in sequence: ( ) → { } → [ ].

Q4. Why is “of” solved before division and multiplication?

Because “of” always represents direct multiplication and has higher priority.

Q5. What is the meaning of modulus in simplification?

Modulus gives the absolute value of a number, always producing a positive result.

Q6. Why does vinculum come before BODMAS operations?

Vinculum groups values at the highest priority and must be solved before brackets.

Q7. Are division and multiplication equal in priority?

Yes, both are solved left to right based on their appearance in the expression.

Q8. When should addition and subtraction be performed?

Only after completing brackets, of, division, and multiplication.

Q9. Why do students frequently make mistakes in simplification?

Because they follow left-to-right blindly without respecting operation priority.

Q10. What is the simplest way to master BODMAS?

Practise expressions regularly while strictly following the order: Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction.

Aptitude

Table of contents

Simplification: Formulas, Concepts, Tricks & Step-by-Step Rules for BODMAS

Quick Overview: Simplification (BODMAS, Modulus, Vinculum) Formulas

Formulas for Simplification (BODMAS, Modulus, Vinculum)

1. BODMAS Formula

2. Bracket Removal Formula

3. “of” Formula (Convert to Multiplication)

4. Division Formula

5. Multiplication Formula

6. Addition & Subtraction Formula

7. Modulus Formula

8. Vinculum Formula (Highest Priority)

Smart Tips and Practical Tricks for Solving Simplification (BODMAS) Problems

1. Always Identify and Solve the Highest-Priority Operation First

2. Remove Brackets in the Correct Order

3. Convert “of” into Multiplication Immediately

4. Solve Vinculum Before Applying BODMAS

5. Handle Modulus Carefully - It Always Produces a Positive Value

6. Perform Division and Multiplication from Left to Right

7. Do Not Add or Subtract Until All Higher Operations Are Over

8. Write a Clean Step-by-Step Breakdown

9. Recognize Common Expression Patterns

10. Practice Exam-Type Expressions Frequently

FAQs About Simplification, BODMAS, Modulus & Vinculum

Q1. Why is BODMAS important in simplification?

Q2. Why must brackets be solved first?

Q3. What is the correct order of bracket removal?

Q4. Why is “of” solved before division and multiplication?

Q5. What is the meaning of modulus in simplification?

Q6. Why does vinculum come before BODMAS operations?

Q7. Are division and multiplication equal in priority?

Q8. When should addition and subtraction be performed?

Q9. Why do students frequently make mistakes in simplification?

Q10. What is the simplest way to master BODMAS?

Related Articles

Table of contents

Simplification: Formulas, Concepts, Tricks & Step-by-Step Rules for BODMAS

Quick Overview: Simplification (BODMAS, Modulus, Vinculum) Formulas

Formulas for Simplification (BODMAS, Modulus, Vinculum)

1. BODMAS Formula

2. Bracket Removal Formula

3. “of” Formula (Convert to Multiplication)

4. Division Formula

5. Multiplication Formula

6. Addition & Subtraction Formula

7. Modulus Formula

8. Vinculum Formula (Highest Priority)

Smart Tips and Practical Tricks for Solving Simplification (BODMAS) Problems

1. Always Identify and Solve the Highest-Priority Operation First

2. Remove Brackets in the Correct Order

3. Convert “of” into Multiplication Immediately

4. Solve Vinculum Before Applying BODMAS

5. Handle Modulus Carefully - It Always Produces a Positive Value

6. Perform Division and Multiplication from Left to Right

7. Do Not Add or Subtract Until All Higher Operations Are Over

8. Write a Clean Step-by-Step Breakdown

9. Recognize Common Expression Patterns

10. Practice Exam-Type Expressions Frequently

FAQs About Simplification, BODMAS, Modulus & Vinculum

Q1. Why is BODMAS important in simplification?

Q2. Why must brackets be solved first?

Q3. What is the correct order of bracket removal?

Q4. Why is “of” solved before division and multiplication?

Q5. What is the meaning of modulus in simplification?

Q6. Why does vinculum come before BODMAS operations?

Q7. Are division and multiplication equal in priority?

Q8. When should addition and subtraction be performed?

Q9. Why do students frequently make mistakes in simplification?

Q10. What is the simplest way to master BODMAS?

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