Simplification
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Quantitative Aptitude - Simplification
Solve expressions quickly and accurately using rules of arithmetic and BODMAS.
1. BODMAS Principles
- Brackets → Order → Division → Multiplication → Addition → Subtraction
- Within brackets, apply the same rule recursively.
2. Operations with Mixed Numbers
- Remove decimals by multiplying numerator and denominator by 10ⁿ.
- Convert fractions to common denominators before adding or subtracting.
3. Fractions and Division
- Division by a fraction is equivalent to multiplication by its reciprocal.
- For nested fractions, invert appropriately to simplify.
4. Exponents and Roots
- Simplify powers using multiplication rules: \( a^m \times a^n = a^{m+n} \).
- Division of powers: \( a^m ÷ a^n = a^{m−n} \).
- Apply root operations: \( \sqrt{a^2} = |a| \).
5. Percent, Ratio, and Proportion
- Convert percentages to fractions or decimals before simplifying.
- Use ratio conversion: \( \frac{a}{b} ÷ \frac{c}{d} = \frac{ad}{bc} \).
6. Quick Tips for Accuracy
- Simplify step by step; don’t skip bracket steps.
- Cancel common factors early in multiplication/division.
- Keep track of signs (positive/negative) carefully.
- In MCQs, approximate intermediate results to eliminate wrong options quickly.
7. Mental Math Shortcuts
- Use distributive property: \( a(b + c) = ab + ac \).
- Recognize perfect squares and cubes to simplify roots faster.
- Use factor pairs to simplify numeric multipliers.
8. Error Avoidance Techniques
- Recheck decimal placements after division or multiplication.
- Validate final answer via approximate estimation.
- Watch parentheses and nested fraction accuracy.
9. Revision Checklist
- Master BODMAS order of operations.
- Be fluent in fraction-decimal-percentage interconversion.
- Practice exponent, root, and ratio simplification regularly.
- Use mental math tricks and error-check methods.
Summary: Follow BODMAS strictly, simplify systematically, use cancellation and mental shortcuts, and verify with estimation. This ensures speed and accuracy in competitive exams.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Area
- Volume & Surface Areas
- Mensuration
- Probability
- Heights & Distances
- Algebra
- Divisibility Rules & Remainder Theorem
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations