18 October, 2017

Simplification Rules for Numerical Calculations







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Simplification Rules

If you know simplification rules, simplification 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, while doing numerical calculations, simplification rules are necessary to follow. Simplification rule is VBODMAS, a complete form of VBODMAS is vinculum bracket of division multiplication addition subtraction.

Operators for Simplification with Example:

Operators for Simplification

NameSymbolExmple
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

OperandOperatorOperandEqual toResult
-×-=+
-×+=-
+×-=-
+×+=+

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,

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.

  1. First priority is vinculum.
  2. Second priority is brackets (), {} and [].
  3. Third priority is OF.
  4. Forth priority is division and multiplication.
  5. Fifth priority is addition and subtraction.
Rajashekar KankanalaRajashekarKankanala
Tuts Raja
NTR Colony
Hyderabad,Telangana,500087India
9110760272
http://www.tutsraja.com/

Tags: General Aptitude, Verbal Reasoning, Static GK, Current Affairs, Computer Basics


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