If you know the rules of simplification, this is an easy topic. Many bank exams focus on simplification. It is a mandatory question, tricky and easy to make mistakes. All simplification questions are based on the BODMAS rule.
Simplification is done by addition, subtraction, multiplication and division. It is necessary to follow the rules of simplification while doing numerical calculations.
The abbreviation of the simplification rule is VBODMAS. The full form of VBODMAS is Vinculum Bracket of Division Multiplication Addition Subtraction.
The Formula for Simplification (VBODMAS):
VBODMAS is a short form to remember the rules of simplification. Here I will tell you one by one in deep importance. Let's see,
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 a vinculum. It is a horizontal line drawn over a group of digits. We can also call it a 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 a bracket. There are three brackets here (), {} and []. Within those brackets we have precedence. The first precedence is the open bracket (). The second precedence is the flower bracket {}. Finally, the third precedence is the 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]
=23Note: Remember the bracket precedence with a little trick. Someone gave you a gift. What you do is, “Open the gift, look at the gift (flowers) and close the gift.”
3. O (of):
O is nothing but OF . We write multiplication * instead of OF . Here multiplication takes precedence after brackets even though OF .
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 are of equal importance. You can do both at the same time.
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 are of 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 addition. Here addition and subtraction have equal priority. You can add the same signs of values at the same time.
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]
=-150
7. S (Subtraction):
S is nothing but subtraction. Here subtraction and addition have equal priority. It is the last priority in the 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, a list of simplification priorities for all numerical calculations.
- First priority is vinculum .
- Second priority is brackets (), {} and [] .
- Third priority is OF .
- Fourth 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
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