TNPSC Group IV · Bite-size lessons

Simplification

About 6 min · Aptitude and Mental Ability Test · English

Time worked out from the lesson's 385 words at 150 words a minute, plus a minute for each question.

Simplification is the foundation of quantitative aptitude for TNPSC Group IV. Every arithmetic problem—whether it involves percentages, interest, or time-work—ultimately requires you to simplify numerical expressions accurately and quickly. This topic tests your command over the order of operations, your fluency with fractions and decimals, and your ability to handle roots.

Key ideas

• BODMAS Rule: Operations must be performed in the order—Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. Division and multiplication are done left to right; same for addition and subtraction.
• Brackets Hierarchy: Solve innermost brackets first. The order is: Vinculum (bar), then Parentheses ( ), then Curly Braces { }, then Square Brackets [ ].
• Fractions: A fraction a/b represents a parts out of b equal parts. To add or subtract fractions, find a common denominator. To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal.
• Decimals: Decimals are fractions with denominators as powers of 10. Converting between fractions and decimals is essential—memorize common conversions like 1/4 = 0.25, 1/8 = 0.125.
• Square Roots: √a is the number which, when squared, gives a. Key values: √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236. Perfect squares up to 625 should be memorized.

Watch out for

• Ignoring left-to-right rule for division and multiplication: Students assume multiplication comes before division. Wrong—they have equal priority; go left to right. Correct: 24 ÷ 4 × 2 = 6 × 2 = 12, not 24 ÷ 8 = 3.
• Forgetting to convert decimals before operating with fractions: Adding 1/3 + 0.5 directly leads to errors. Always convert 0.5 to 1/2 first, then find common denominator.
• Wrong bracket order: Solving [ ] before ( ) is incorrect. Always start from innermost bracket regardless of type.

Quick reference

• BODMAS: Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction (L→R)
• "Of" = Multiplication: Solve "of" immediately after brackets
• Fraction division: Flip the second fraction and multiply
• LCM for fraction addition: Always find least common denominator before adding or subtracting
• Memorize roots: √2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24; cubes up to 10³ = 1000

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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