If you know **simplification rules**, it is an easy topic. Many bank exams focusing on simplification. It is a **compulsory question**, tricky and easy to make mistakes. All simplification questions are based on **BODMAS rule**.

Simplification is done by addition, subtraction multiplication and division. Simplification rules are necessary to follow, while doing **numerical calculations**.

Short form of Simplification rule is **VBODMAS**. Full form of VBODMAS is vinculum bracket of division multiplication addition subtraction.

### The Formula for Simplification (VBODMAS):

VBODMAS is a short form for **remembering** simplification rules. Here I will tell one by one in depth **priority**.

Let's see,

**Note: **Click on show/hide button to show index of the content.

1. V (Vinculum)

2. B (Bracket)

3. O (of)

4. D (Division)

5. M (Multiplication)

6. A (Addition)

7. S (Subtraction)

Speed Addition Tricks

#### 1. V (Vinculum):

V is nothing but **vinculum**. It is a horizontal line, drawn over a group of digits. We can also call **bar**. It is the first priority in simplification.

**Example: **
32 - [5 - 8 * 5 + 6 - 3]

=32 - [5 - 8 * 5 + 6 - 3][∴ Simplify 5 and 6]

=32 - [5 - 8 * 11 - 3][∴ Simplify 8 and 11]

=32 - [5 - 88 - 3][∴ Add equal signs]

=32 - [5 - 91][∴ Perform subtraction]

=32 - [- 86][∴- × - = +]

=32 + 86[∴ perform addition]

=118

#### 2. B (Bracket):

B is nothing but **bracket**. Here three brackets are there (), {} and []. We have a priority among those brackets. First **priority** is open bracket (). The second priority is flower bracket {}. Finally, third priority is a closed bracket.

**Example:** 8 - [3 + {7 - (9 - 5)}] +5^2

8 - [3 + {7 - (9 - 5)}] +5^2[∴Simplify open bracket 9, 5 ]

=8 - [3 + {7 – 4}] + 25[∴Simplify flower bracket]

=8 - [3 + 3] +25[∴Simplify closed bracket]

=8 – [6] +21[∴add same signs]

=29 - [6][∴Perform subtraction]

=23

**Note:** remember bracket priority with **small trick**. Someone gave you a gift. What will you do, “just open gift, see gift (flowers) and close the gift.

#### 3. O (of):

O is nothing but **OF**. We write Multiplication *, Instead of OF. Here first priority is OF after brackets even though **multiplication**.

**Example:** 49 ÷ 7 × 4 ÷ 2 + 5 of 63 ÷ 3

49 ÷ 7 × 4 ÷ 2 + 5 of 63 ÷ 3[∴Perform OF 5, 63]

=49 ÷ 7 × 4 ÷ 2 + 315 ÷3[∴Perform division]

=7 × 2 + 105[∴Perform multiplication]

=14 + 105[∴Perform addition]

=119

#### 4. D (Division):

D is nothing but **division**. Here **division and multiplication** is the equal priority. You can do both simultaneously.

**Example:** 36 ÷ 6 × 25% × 4 + ½ of 100 ÷ 5

36 ÷ 6 × 25% × 4 + ½ of 100 ÷ 5[∴Perform OF ½, 100]

=36 ÷ 6 × 25 / 100 × 4 + 50 ÷5[∴Perform division]

=6 × 1 / 4 × 4 + 10[∴Perform division]

=6 + 10[∴Perform addition]

=16

#### 5. M (Multiplication):

M is nothing but **multiplication**. Here division and multiplication is the equal priority after **OF**.

**Example:** 5 × [-12 × (121 ×11) - (-4) × {3 – 1 - 3}]

5 × [-12 × (121 × 11) - (-4) × {3 – 1 - 3}][∴Simplify open bracket]

=5[-12 × 1331 + 4 × {3 - 1 -3}][∴Simplify flower bracket]

=5[-12 × 1331 + 4 × {-1}][∴Perform multiplication]

=5[-15972 - 4][∴Add values of equal signs]

=5[-15976][∴Perform multiplication]

=79880

#### 6. A (Addition):

A is nothing but an **addition**. Here **addition and subtraction** is the equal priority. You can add same signs of values simultaneously.

**Example:** 3 - [22 + (46 + 77) - {3 - 11}]

3 - [22 + (46 + 77) - {3 - 11}][∴Simplify open bracket]

=3 - [22 + 123 - {3 - 11}][∴Simplify flower bracket]

=3 - [22 + 123 - {-8}][∴Add values of equal signs]

=3 - [145 + 8][∴Perform addition]

=3 - [153][∴Perform Subtraction]

=-153

#### 7. S (Subtraction):

S is nothing but **Subtraction**. Here Subtraction and addition is the equal priority. It is **last priority** in calculation of numbers.

**Example:** 3 - 45 + 19 + 77 - 17 – 11

3 - 45 + 19 + 77 - 17 – 11[∴Add values of equal signs]

=99 - 73[∴Perform subtraction]

=26

Remember: **VBODMAS** = Vinculum Bracket Of Division Multiplication Addition Subtraction

### Remember Key points:

Finally, simplification priority list for all numerical calculations.

- First priority is
**vinculum**. - Second priority is
**brackets**(), {} and []. - Third priority is
**OF**. - Forth priority is
**division**and**multiplication**. - Fifth priority is
**addition**and**subtraction**.

### Operators for Simplification with Example:

**Operators for Simplification**

Name | Symbol | Exmple |
---|---|---|

Addition | + | a + b |

Subtraction | - | a - b |

Multiplication | × | a × b |

Division | / | a / b |

Percentage | % | a% |

Of | × | a of b |

Vinculum | abc | a + b + c |

### Operator Sign Table

**Sign Table**

Operand | Operator | Operand | Equal to | Result |
---|---|---|---|---|

- | × | - | = | + |

- | × | + | = | - |

+ | × | - | = | - |

+ | × | + | = | + |

Speed Addition Tricks