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Simplification & Approximation

BODMAS, fractions, decimals and approximation tricks for fast arithmetic.

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Simplification & Approximation — Core

Simplification core — BODMAS, fractions, decimals
Notes

Simplification questions test whether you can apply the BODMAS order quickly and accurately. RRB NTPC reserves 5–8 marks for this in every shift.

The BODMAS order: Brackets → Order (powers, roots) → Division and Multiplication (left to right) → Addition and Subtraction (left to right).

Note that ÷ and × have the same priority — work left to right. The same is true for + and −. A common trap: 12 ÷ 3 × 2 is not 12 ÷ 6 = 2; it is (12 ÷ 3) × 2 = 8.

Bracket order inside a problem: bar (vinculum) → ( ) → { } → [ ]. Solve the innermost first.

Fraction essentials:

  • To add/subtract, get a common denominator: 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
  • To multiply: numerators × numerators, denominators × denominators. Cancel first to keep numbers small.
  • To divide by a fraction, multiply by its reciprocal: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4.

Decimals:

  • 0.25 = 1/4, 0.125 = 1/8, 0.2 = 1/5, 0.4 = 2/5, 0.6 = 3/5, 0.75 = 3/4. Memorise these — they convert ugly decimals into clean fractions.
  • For repeating decimals like 0.333…, recognise it as 1/3.

Percentage shortcuts:

  • 10% = ÷10, 1% = ÷100, 25% = ÷4, 50% = ÷2, 12.5% = ÷8, 20% = ÷5.
  • x% of y = y% of x — use this when one side is easier (e.g. 14% of 50 = 50% of 14 = 7).
Approximation tricks & worked examples
Worked example

In RRB NTPC most "simplification" questions are actually approximation — you round numbers to make the arithmetic doable in 20 seconds.

Rule of thumb: round to the nearest convenient figure (multiple of 10, 25, or a clean fraction) and check that the rounding errors roughly cancel.

Example 1 — approximation:
(24.97% of 800) + (39.98% of 250) − 49.9 = ?
→ ≈ 25% × 800 + 40% × 250 − 50 = 200 + 100 − 50 = 250.

Example 2 — fractions:
(3/7 of 567) ÷ (2/9 of 270) = ?
3/7 of 567 = 243. 2/9 of 270 = 60. 243 ÷ 60 = 4.05.

Example 3 — square roots:
√1764 = ? Try 40² = 1600, 42² = 1764. Answer: 42. Memorise squares up to 30 and cubes up to 15.

Example 4 — BODMAS trap:
125 + 25 × 4 − 100 ÷ 5 = 125 + 100 − 20 = **205** (multiply/divide first, then add/subtract).

Speed tactics:

  1. Scan all options first — if they are far apart, you can approximate aggressively.
  2. Convert percentages to fractions where possible: 33⅓% = 1/3, 16⅔% = 1/6, 11⅑% = 1/9.
  3. Spot patterns: if every option is between 200 and 250, you only need a 2-digit answer.
  4. Skip if a calculation has ≥4 operations and ≥3-digit numbers — return at the end.