Fractions and Decimals

• Introduction

  • Definition of Fractions (Part of a whole)
  • Definition of Decimals (Fraction with base 10 denominator)

• Fractions

  • Types of Fractions
    • Proper Fractions (Numerator < Denominator)
    • Improper Fractions (Numerator > Denominator)
    • Mixed Fractions (Combination of whole number and proper fraction)
    • Equivalent Fractions (Same value, different numbers)
  • Operations on Fractions
    • Addition and Subtraction
      • Like fractions (direct operation)
      • Unlike fractions (find LCM of denominators)
    • Multiplication of Fractions
      • Fraction by a whole number
      • Fraction by a fraction (Numerator $\times$ Numerator, Denominator $\times$ Denominator)
      • Operator "Of" means multiplication
    • Division of Fractions
      • Reciprocal of a fraction (multiplicative inverse)
      • Division by multiplying the reciprocal

• Decimals

  • Place Value in Decimals
    • Tenths ($\frac{1}{10}$)
    • Hundredths ($\frac{1}{100}$)
    • Thousandths ($\frac{1}{1000}$)
  • Comparison of Decimals
    • Compare whole number part first
    • Compare tenth, hundredth parts sequentially
  • Operations on Decimals
    • Addition and Subtraction
      • Align decimal points vertically
    • Multiplication of Decimals
      • Multiply normally, then count and place decimal point for total decimal places
      • Multiplying by 10, 100, 1000 (shift decimal right)
    • Division of Decimals
      • Division by whole numbers
      • Division by decimals (convert divisor to whole number by shifting decimal)
      • Dividing by 10, 100, 1000 (shift decimal left)

• Applications and Units

  • Conversion of Units
    • Length: cm to m, m to km
    • Weight: g to kg
    • Money: paise to rupees