In-Depth: Simplification & BODMAS
CLAT Application & Relevance
Importance: High (Indirect). While rarely tested as standalone problems, the principles of Simplification and BODMAS (or PEMDAS/BEDMAS) are absolutely fundamental. Every single calculation you do in Data Interpretation or any other quantitative problem relies on correctly applying these rules. Mistakes here lead to incorrect answers even if your core concept (percentage, ratio, etc.) is correct.
How it's tested: Implicitly in every calculation. Complex numbers, fractions, decimals, and operations (multiplication, division, addition, subtraction) will be present in DI sets. Your speed and accuracy in performing these operations, following the correct order, is paramount.
Section 1: Core Concepts & BODMAS Rule
Simplification refers to reducing an algebraic expression or a numerical calculation to its simplest form. The BODMAS (or PEMDAS) rule provides the correct order of operations for arithmetic expressions.
The BODMAS Rule
BODMAS is an acronym that dictates the sequence of operations to be followed while solving mathematical expressions. Any deviation from this order will result in incorrect answers.
- B - Brackets (Parentheses in PEMDAS). Solve operations inside brackets first:
(), {}, []. - O - Orders (Exponents/Indices in PEMDAS). Solve powers, square roots, etc.
- D - Division
- M - Multiplication
- A - Addition
- S - Subtraction
Note: Division and Multiplication have the same priority. Solve them from left to right. Similarly, Addition and Subtraction have the same priority; solve them from left to right.
Tips for Efficient Simplification:
- Know your Tables: Up to 20.
- Squares and Cubes: Memorize squares up to 30 and cubes up to 15.
- Fractions & Decimals: Be comfortable with conversions and operations.
- Approximation: For certain questions, especially in DI, approximating values can save time. However, be careful not to approximate if the options are very close.
- Practice Mental Math: Develop speed for basic arithmetic operations.
Section 2: Solved CLAT-Style Examples (Application in Calculation)
Example 1: Applying BODMAS to a Numerical Expression
Passage Context: "A legal analyst was calculating a firm's quarterly expenses. One part of the calculation involved simplifying the following expression:"
Question: "Simplify: 45 ÷ 5 + 3 × (7 - 2)²"
Detailed Solution:
1. Brackets (Parentheses) First:
(7 - 2) = 5
Expression becomes: 45 ÷ 5 + 3 × (5)²
2. Orders (Exponents):
(5)² = 25
Expression becomes: 45 ÷ 5 + 3 × 25
3. Division:
45 ÷ 5 = 9
Expression becomes: 9 + 3 × 25
4. Multiplication:
3 × 25 = 75
Expression becomes: 9 + 75
5. Addition:
9 + 75 = 84
Answer: The simplified value of the expression is 84.
Example 2: Simplification with Fractions and Mixed Operations (DI Context)
Passage Context: "A survey found that 1/4 of law students prefer criminal law, 1/3 prefer corporate law, and the remaining prefer human rights law. If the total number of students surveyed was 600, and 1/5 of the human rights law enthusiasts are female."
Question: "How many female students prefer human rights law?"
Detailed Solution:
1. Students preferring Criminal Law: (1/4) * 600 = 150
2. Students preferring Corporate Law: (1/3) * 600 = 200
3. Total preferring Criminal or Corporate: 150 + 200 = 350
4. Students preferring Human Rights Law (Remaining): 600 - 350 = 250
5. Female students preferring Human Rights Law: (1/5) * 250
= 50.
Answer: There are 50 female students who prefer human rights law.