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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.

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