Cheat Sheet: Simplification
Simplification is a high-scoring and foundational topic in bank examinations as it tests speed, accuracy, and command over basic arithmetic operations like BODMAS, fractions, percentages, roots, and powers. This topic directly contributes to performance in Number Series, Approximation, and Data Interpretation. In the Preliminary examination, Simplification usually carries a weightage of 5-10 questions (approximately 10-15 marks) and can be solved quickly using approximation techniques, while in the Mains examination, it appears in a more calculation-intensive form with 3-5 questions. Due to its relatively low difficulty level and high return on time invested, mastering Simplification significantly boosts overall score and helps in clearing sectional and overall cut-offs.
1. BODMAS Rule
B - Brackets
O - Orders (Powers, Roots)
D - Division
M - Multiplication
A - Addition
S - Subtraction
Division and multiplication are solved left to right. Addition and subtraction are solved left to right.
2. Types of Brackets (Priority)
- \(( )\)
- \(\{ \}\)
- \([ ]\)
3. Fractions - Important Rules
\( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \)
Always simplify common factors before multiplication.
4. Decimals - Shortcuts
- \(0.5 = \frac{1}{2}\)
- \(0.25 = \frac{1}{4}\)
- \(0.125 = \frac{1}{8}\)
5. Squares (Important)
| Number | Square |
|---|---|
| 11 | \(121\) |
| 12 | \(144\) |
| 13 | \(169\) |
| 14 | \(196\) |
| 15 | \(225\) |
| 16 | \(256\) |
| 17 | \(289\) |
| 18 | \(324\) |
| 19 | \(361\) |
| 20 | \(400\) |
| 25 | \(625\) |
| 30 | \(900\) |
6. Cubes
| Number | Cube |
|---|---|
| 2 | \(8\) |
| 3 | \(27\) |
| 4 | \(64\) |
| 5 | \(125\) |
| 6 | \(216\) |
| 7 | \(343\) |
| 8 | \(512\) |
| 9 | \(729\) |
| 10 | \(1000\) |
7. Square Roots
\(\sqrt{4}=2,\ \sqrt{9}=3,\ \sqrt{16}=4,\ \sqrt{25}=5,\ \sqrt{36}=6\)
\(\sqrt{49}=7,\ \sqrt{64}=8,\ \sqrt{81}=9,\ \sqrt{100}=10\)
8. Percentage Shortcuts
- \(10\% = \frac{1}{10}\)
- \(20\% = \frac{1}{5}\)
- \(25\% = \frac{1}{4}\)
- \(50\% = \frac{1}{2}\)
- \(75\% = \frac{3}{4}\)
\( x\% \text{ of } y = y\% \text{ of } x \)
9. Approximation
\(498 \approx 500\)
\(19.8 \approx 20\)
10. Laws of Exponents
\( a^0 = 1 \) \( a^{-n} = \frac{1}{a^n} \) \( a^m \times a^n = a^{m+n} \) \( \frac{a^m}{a^n} = a^{m-n} \)
11. Common Mistakes
- Ignoring BODMAS
- Wrong order of division and multiplication
- Not simplifying fractions early
- Over-calculating when approximation is enough
FAQs on Cheat Sheet: Simplification
| 1. What is the BODMAS rule and how does it apply in mathematical calculations? |  |
| 2. What are the different types of brackets and their priority in calculations? | |
| 3. What are the important rules to remember when working with fractions? | |
| 4. How can shortcuts be applied when working with decimals? | |
| 5. What are the laws of exponents and how do they aid in simplification? | |
