BODMAS & VBODMAS Rules

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Ex: Solve 12 + 8 ÷ 4

Sol: Solⁿ is as follows = 12 + 8 ×(1/4) = 12 + 2 = 14

Note: Many students incorrectly solve 12 + 8 ÷ 4 as 20 ÷ 4 = 5. This is wrong because they ignore the BODMAS rule. According to BODMAS, division must be done before multiplication and addition. While solving simplification questions, always follow the correct sequence to avoid mistakes and get accurate answers.

VBODMAS & BODMAS Rules

V = Vinculum (Bar / Overline)

This rule includes V because some questions contain a bar like: 6+4‾ bar on top or use bracket

Order becomes:

1. V → Vinculum (Bar), A bar is used to group numbers without using brackets.


2. B → Bracket


3. O → Order ( Powers, roots )


4. D → Division


5. M → Multiplication


6. A → Addition


7. S → Subtraction

BODMAS

No Vinculum. Used when no bar is present.

1. B → Bracket


2. O → Order (powers, roots)


3. D → Division


4. M → Multiplication


5. A → Addition


6. S → Subtraction

Final Simple Rule

If the expression has a bar (overline) → use VBODMAS

If no bar → use BODMAS

VBODMAS Rule

1. Simple Bodmas Example

Q: 12 + 6 ÷ 3

1^st : Division first : 6 ÷ 3 = 2

2^nd  Now add : 12 + 2 = 14

Ans = 14

Q. 50 - 5×2 + 10 + 2

Follow BODMAS / PEMDAS rule: Brackets → Orders → Division → Multiplication → Addition → Subtraction

1. Multiply first: 5×2 =10


2. Substitute back: 50 -10 +10 + 2


3. Now go left to right for + and - : 50 -10 = 40, 40 + 10 = 50, 50 + 2 = 52

Ans : 52

2. Medium Bodmas Example

Q. 20 - 4 × (10 ÷ 2)

1^st : Solve bracket first: 10 ÷ 2 = 5

Now expression becomes: 20 – 4 × 5

2^nd : Multiplication: 4 × 5 = 20

3^rd : Subtraction: 20 – 20 = 0

Ans = 0

3. Tough Bodmas Example

Solve:

40 − [6 + {12−4×(18÷3)}] ÷ 2

Solⁿ

1^st Solve the innermost bracket ( )

Inside ( ) we have: 18÷3 = 6

Now the expression becomes: 40 − [6+{12−4×6}]÷2

2^nd Multiplication next : 4 × 6 = 24

Now: 40 - [6+{12−24}] ÷ 2

3^rd  Solve curly bracket { } : 2−24 = −12, Now 40 - [6+(−12)] ÷ 24

4^th Solve square bracket [ ] : 6 + (−12) = −6 , So we get: 40 - (-6) ÷ 2

5^th Division first : (−6) ÷ 2 = −3, Now: 40 - (-3)

6^th  Subtraction becomes addition : 40 + 3 = 43

Ans = 43

Q. VBODMAS Example: Simplify the expression: 18 – [6 – {4 – (8 – 6 + 3  )}], bar on above 6 + 3

Sol: This is an example where brackets are given. Brackets are solved after Bar. The order of Solving the brackets is (), {} and [] respectively. So, the solution of above examples is as follows.
= 18 – [6 - {4 – (8 – 9)}] ⇒ 18 – [6 – {4 – (- 1)}]
= 18 – [6 - {4 + 1}] ⇒ 18 – [ 6 – 5] ⇒ 18 – [ 1] = 18 – 1 = 17