Fractions and Decimals

Master fractions and decimals for RRB exam preparation with comprehensive concepts and practice problems.

Basic Concepts

Fractions

Definition and Types

• Proper Fraction: Numerator < Denominator (e.g., 3/4)
• Improper Fraction: Numerator > Denominator (e.g., 7/4)
• Mixed Fraction: Whole number + Proper fraction (e.g., 2 3/4)
• Equivalent Fractions: Different fractions representing same value

Fraction Operations

Addition and Subtraction

• Find common denominator
• Convert to equivalent fractions
• Add/subtract numerators
• Simplify result

Multiplication

• Multiply numerators
• Multiply denominators
• Simplify result

Division

• Invert the second fraction
• Multiply as usual
• Simplify result

Decimals

Types of Decimals

• Terminating Decimals: Finite decimal places (e.g., 0.75)
• Recurring Decimals: Repeating pattern (e.g., 0.333…, 0.142857…)
• Mixed Decimals: Combination of terminating and recurring

Decimal Operations

• Addition/Subtraction: Align decimal points
• Multiplication: Count total decimal places
• Division: Remove decimals, then divide

Important Formulas

Fraction to Decimal Conversion

• Method: Divide numerator by denominator
• Terminating: Denominator factors of 2 and/or 5 only
• Recurring: Other prime factors in denominator

Decimal to Fraction Conversion

• Terminating: Write as fraction with power of 10 denominator
• Recurring: Use algebraic method

Simplification Rules

• Divisibility by 2: Last digit even
• Divisibility by 3: Sum of digits divisible by 3
• Divisibility by 5: Last digit 0 or 5
• Divisibility by 9: Sum of digits divisible by 9

Practice Problems

Question 1

Convert 3/8 to decimal form.

Question 2

Add: 2 3/4 + 1 5/6

Question 3

Multiply: 3 1/2 × 2 2/3

Question 4

Divide: 7 1/2 ÷ 2 1/4

Question 5

Convert 0.375 to fraction form.

Question 6

Add: 0.25 + 0.125 + 0.75

Question 7

Multiply: 0.2 × 0.3 × 0.4

Question 8

Find the value of 0.6̅ (0.666…).

Question 9

Compare: 3/8 and 0.375

Question 10

Simplify: (2 1/3 - 1 1/6) ÷ 1/2

Quick Tips

Mental Calculations

• Halves: 1/2 = 0.5, 1/4 = 0.25
• Thirds: 1/3 = 0.33…, 2/3 = 0.66…
• Quarters: 1/4 = 0.25, 3/4 = 0.75
• Fifths: 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8

Common Fractions

• 1/2: 50%, 0.5
• 1/3: 33.33%, 0.33…
• 1/4: 25%, 0.25
• 1/5: 20%, 0.2
• 1/8: 12.5%, 0.125
• 1/16: 6.25%, 0.0625

Back to Maths Topics

All Topic Practice