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Important Formula
Simplification and approximation are crucial topics in quantitative aptitude, commonly tested in competitive exams. Mastering these formulas can help you solve problems quickly and accurately.
1. Basic Arithmetic Operations
Addition & Subtraction
Commutative Property:
a + b = b + a
a - b ≠ b - a
Associative Property:
(a + b) + c = a + (b + c )
Multiplication & Division
Commutative Property:
a × b = b × a
a ÷ b ≠ b ÷ a
Associative Property:
(a × b) × c = a × (b × c)
Distributive Property:
a × (b + c) = a × b + a × c
a × (b - c) = a × b - a × c
2. BODMAS Rule (Order of Operations)
The order in which operations should be performed:
B – Brackets
O – Orders (Powers & Roots)
D – Division
M – Multiplication
A – Addition
S – Subtraction
Example:
5 + 3 × (8 ÷ 2)2
= 5 + 3 × (4)2
= 5 + 3 × 16
= 5 + 48
= 53
3. Percentage Formulas
x% of y = (x/100) × y
y is what % of x = (y/x) × 100
Percentage Increase/Decrease:
[(New Value - Original Value)/Original Value] × 100
4. Fraction-Decimal-Percentage Conversions
5. Approximation Techniques
Rounding Off Numbers:
If the next digit is ≥5, round up.
If the next digit is <5, round down.
Example: 4.68 ≈ 4.7 (to 1 decimal place)
Estimating Sums/Differences:
498 + 372 ≈ 500 + 370 = 870Estimating Products:
49 × 31 ≈ 50 × 30 = 1500
6. Square & Cube Shortcuts
Squares (1-30)
Cubes (1-10)
| Number | Cube |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
7. Square Root & Cube Root Approximations
√2 ≈ 1.414
√3 ≈ 1.732
√5 ≈ 2.236
√10 ≈ 3.162
Cube root of 2 ≈ 1.26
Cube root of 3 ≈ 1.442
8. Algebraic Identities
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
a2 - b2 = (a + b)(a - b)
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a - b)3 = a3 - 3a2b + 3ab2 - b3
9. Divisibility Rules
| Number | Rule |
|---|---|
| 2 | Last digit is even (0,2,4,6,8) |
| 3 | Sum of digits divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Ends with 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits divisible by 8 |
| 9 | Sum of digits divisible by 9 |
| 10 | Ends with 0 |
| 11 | Difference (sum of odd & even digits) divisible by 11 |
Final Tips:
Practice mental math for faster calculations.
Use approximation when exact computation is time-consuming.
Memorize key squares, cubes, and roots for quick solving.
This guide covers essential formulas to tackle simplification and approximation problems efficiently. Keep practicing to improve speed and accuracy!
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FAQs on Simplification: Important Formula: - IBPS PO Prelims & Mains Preparation - Bank Exams
| 1. What are the basic arithmetic operations used in mathematics? |  |
Ans. The basic arithmetic operations are addition, subtraction, multiplication, and division. These operations form the foundation of all mathematical calculations.
| 2. How does the BODMAS rule affect the order of operations in calculations? | |
Ans. The BODMAS rule stands for Brackets, Orders (i.e., powers and roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This rule helps determine the correct order to perform operations to get the right answer in complex calculations.
| 3. How can I calculate the percentage of a number easily? | |
Ans. To calculate the percentage of a number, you can use the formula: Percentage = (Part/Total) x 100. For example, to find 20% of 50, calculate (20/100) x 50 = 10.
| 4. What are some quick techniques for approximating square and cube roots? | |
Ans. For square roots, you can use the nearest perfect square method. For example, to approximate √50, notice that √49 = 7, so √50 is slightly more than 7. For cube roots, you can find the nearest perfect cube. For instance, the cube root of 27 is 3, and since 28 is close to 27, you can estimate that the cube root of 28 is slightly more than 3.
| 5. What are the key algebraic identities I should remember for bank exams? | |
Ans. Some key algebraic identities include:
1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. a² - b² = (a + b)(a - b)
4. (a + b + c)² = a² + b² + c² + 2(ab + ac + bc)
These identities can simplify complex expressions and make calculations easier during exams.
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