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Simplification — BODMAS, Fractions, and Fast Calculation | TNPSC, SSC, Bank

Learn simplification shortcuts using BODMAS, fractions, decimals, surds, and approximation with worked aptitude examples.

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Quick Concept Summary

Simplification questions test accuracy under time pressure. Most mistakes come from ignoring the order of operations or converting fractions too late.

Core Rules

RuleExample
Brackets first(18 + 6) / 3 = 8
Division and multiplication left to right24 / 6 x 2 = 8
Convert percentages early25% of 240 = 1/4 x 240 = 60

Worked Examples

Example 1

36 / 6 x 4 + 8 = 6 x 4 + 8 = 32

Example 2

3/5 of 250 + 20% of 150 = 150 + 30 = 180

Example 3

sqrt(144) + 18 / 3 = 12 + 6 = 18

Shortcuts

  • Memorise common squares up to 30.
  • Replace 12.5%, 25%, 50%, and 75% with 1/8, 1/4, 1/2, and 3/4.
  • Keep decimal conversion for the final step when fractions are cleaner.

Practice Questions

1. Simplify 48 / 8 x 5 - 6. 2. Find 35% of 400 + 3/4 of 80. 3. Simplify sqrt(225) + 64 / 8. 4. Evaluate (18 + 12) / 5 x 4.

Common Mistakes

  • Doing addition before multiplication
  • Reading of as a separate operation instead of multiplication
  • Rounding too early

Frequently Asked Questions

Resolve brackets first, then powers or roots, then division and multiplication from left to right, then addition and subtraction.

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