Headline: Simplification Made Easy – BODMAS, Fractions, Decimals, Powers and Seven Fully Worked Examples
Simplification is listed under Unit I of the official TNPSC Group IV Aptitude syllabus. Understanding the correct order of arithmetic operations helps you solve lengthy expressions quickly and accurately. This lesson brings together the main SSLC-level rules used in simplification.
1. What is Simplification? Simplification means evaluating an expression containing addition (+), subtraction (−), multiplication (×), division (÷), brackets and powers in the correct order to obtain a simpler result. The order of operations is essential.
2. BODMAS – Correct Order of Operations B – Brackets. O – Orders (powers and roots). D/M – Division and Multiplication have EQUAL priority. A/S – Addition and Subtraction have EQUAL priority. Important: Work from LEFT TO RIGHT when operations have equal priority. It is wrong to assume that division always comes before multiplication, or addition always before subtraction. The word 'of' usually means multiplication: 1/2 of 20 = (1/2) × 20 = 10. Use brackets to clarify ambiguous expressions.
3. Brackets and Sign Rules ( ) – round brackets; [ ] – square brackets; { } – curly brackets. Evaluate the innermost brackets first and work outwards. +(+a)=+a; +(−a)=−a; −(+a)=−a; −(−a)=+a. For multiplication/division, matching signs give a positive answer; different signs give a negative answer.
4. Rules for Fractions Addition/subtraction: Convert fractions to a common denominator, usually using LCM. a/b + c/d = (ad + bc)/bd; a/b − c/d = (ad − bc)/bd. Multiplication: a/b × c/d = ac/bd. Division: a/b ÷ c/d = a/b × d/c (c ≠ 0). Mixed fraction: 2 1/2 = (2×2+1)/2 = 5/2. Reduce the final fraction to its simplest form. A denominator cannot be zero.
5. Decimals and Percentage Conversions 0.5 = 1/2; 0.25 = 1/4; 0.125 = 1/8; 0.75 = 3/4. When dividing decimals, move the decimal point in BOTH the dividend and divisor by the same number of places so the divisor becomes a whole number: 2.4 ÷ 0.6 = 24 ÷ 6 = 4. To convert a percentage into a fraction: 25% = 25/100 = 1/4. Percentages were covered on Day 01; this is only a useful conversion for simplification.
6. Powers, Squares and Square Roots 3² = 3×3 = 9; 2³ = 2×2×2 = 8; √144 = 12 (principal square root). aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0); (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 (a ≠ 0). Be careful: −3² = −(3²) = −9, but (−3)² = 9. Brackets change the result.
7. Time-Saving Methods • Cancel common factors before multiplying: (25×48)÷15 = 5×16 = 80. • Use LCM for adding/subtracting fractions and cross-cancellation for multiplying fractions. • 25×n = (100×n)÷4; 125×n = (1000×n)÷8. • To divide by 5, multiply by 2 and divide by 10. • Use estimation to check whether an answer is reasonable. An approximate answer is not an exact answer.
8. Seven Fully Worked Examples
Example 1 – BODMAS 48 ÷ 6 × (3 + 1) − 5 = 48 ÷ 6 × 4 − 5 [brackets first] = 8 × 4 − 5 [division/multiplication left to right] = 32 − 5 = 27. Answer: 27.
Example 2 – Nested Brackets 18 − [6 + {12 ÷ (2 + 1)}] = 18 − [6 + {12 ÷ 3}] = 18 − [6 + 4] = 18 − 10 = 8. Answer: 8.
Example 3 – Fractions 3/4 + 5/6 − 1/3 LCM of 4, 6 and 3 = 12. = 9/12 + 10/12 − 4/12 = 15/12 = 5/4 = 1 1/4. Answer: 5/4.
Example 4 – Division of a Mixed Fraction 2 1/2 ÷ (5/8) = 5/2 ÷ 5/8 = 5/2 × 8/5 = 8/2 = 4. Answer: 4.
Example 5 – Decimals 2.4 ÷ 0.6 + 1.25 × 4 = 4 + 5 = 9. Answer: 9.
Example 6 – Powers and Square Roots 3² + √144 ÷ 3 − 2³ = 9 + 12 ÷ 3 − 8 = 9 + 4 − 8 = 5. Answer: 5.
Example 7 – Negative Numbers 12 − 3 × (−4) + (−18) ÷ 6 = 12 − (−12) + (−3) = 12 + 12 − 3 = 21. Answer: 21.
9. Common Exam Mistakes • 24 ÷ 6 × 2 = 8, NOT 2. Evaluate equal-priority operations from left to right. • 5 − (2 − 7) = 5 − (−5) = 10. Do not overlook the minus sign before brackets. • 1/2 + 1/3 = 5/6, NOT 2/5. Do not add numerators and denominators separately. • Division by zero is undefined. • −3² and (−3)² have different values.
10. One-Minute Revision Brackets → Powers/Roots → Division/Multiplication left to right → Addition/Subtraction left to right. Fractions: use LCM for addition; multiply by the reciprocal for division. Decimals: shift both decimal points equally when dividing. Negative × Negative = Positive. Estimation is a checking tool, not a replacement for an exact answer.
11. Textbook References and Book-Back Progress Official syllabus: TNPSC Group IV, Part B, Aptitude, Unit I – Simplification (SSLC standard). Relevant Tamil Nadu Samacheer Kalvi textbooks: Class 6 Mathematics, Term 1, Chapter 1 – Numbers (BODMAS and whole-number operations); Class 6, Term 3 – Fractions; and relevant Number System sections of Class 7 Mathematics. Class 6, Term 1, Chapter 1, Exercise 1.3 has been identified as relevant to the order of operations through secondary textbook guides. However, the full exercise and its question count have NOT yet been verified directly against the current original government textbook. Verified book-back questions completed: 0. Total: not yet verified. The seven examples above are original instructional examples; none is presented as an official textbook question or TNPSC PYQ. This lesson covers the main foundational forms of simplification. Ratio and Proportion, Interest, Area, Volume, Time and Work, Reasoning and Puzzles remain to be studied.
The 7 PM practice will have 15 questions (8 General Tamil, 5 General Science, 2 Aptitude) from today's lessons. ETN News – Learn daily, practise consistently!
