Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 3
Chapter 3 of 31

Decimals & Fractions

Converting between decimals and fractions, and the operation rules for each, tested throughout Simplification and DI questions.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Types of Fractions

TypeFeature
Proper FractionNumerator < Denominator (e.g., 3/4)
Improper FractionNumerator ≥ Denominator (e.g., 7/4)
Mixed FractionWhole number + proper fraction (e.g., 1¾)
Like FractionsSame denominator (e.g., 2/5, 3/5)
Unlike FractionsDifferent denominators (e.g., 2/5, 3/7)

Decimal ↔ Fraction Conversion

FractionDecimal
1/20.5
1/40.25
1/50.2
1/80.125
1/30.333… (recurring)
1/60.1666… (recurring)

Operations on Fractions

  • Addition/Subtraction: Convert to a common denominator (LCM of denominators) first
  • Multiplication: Multiply numerators together and denominators together directly
  • Division: Multiply by the reciprocal of the second fraction

Comparing Fractions

Cross-multiply: for a/b vs c/d, compare a×d with b×c — the fraction with the larger cross-product is larger.

💡 Recurring decimal shortcut: 0.3 = 1/3, 0.6 = 2/3, 0.142857 = 1/7

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