Fractions

• Introduction to Fraction
  • Definition: Part of a whole
  • Representation: $\frac{\text{Numerator}}{\text{Denominator}}$
  • Numerator: Number of parts taken
  • Denominator: Total equal parts divided
• Types of Fractions
  • Proper Fraction
    • Numerator < Denominator
    • Value is less than 1 (e.g., $\frac{2}{3}$)
  • Improper Fraction
    • Numerator > Denominator
    • Value is greater than or equal to 1 (e.g., $\frac{5}{3}$)
  • Mixed Fraction
    • Combination of a whole number and a proper fraction (e.g., $1\frac{2}{3}$)
    • Conversion between Improper and Mixed fractions
• Equivalent Fractions
  • Definition: Fractions representing the same value
  • Method: Multiplying or dividing numerator and denominator by the same non-zero number
  • Checking equivalence: Using cross multiplication
• Simplest Form (Lowest Terms)
  • Definition: Fraction with no common factor other than 1
  • Method: Divide numerator and denominator by their HCF
• Like and Unlike Fractions
  • Like Fractions: Fractions with the same denominators (e.g., $\frac{1}{5}, \frac{3}{5}$)
  • Unlike Fractions: Fractions with different denominators (e.g., $\frac{1}{3}, \frac{1}{4}$)
• Operations on Fractions
  • Addition of Like Fractions
    • Add numerators, keep denominator same ($\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$)
  • Subtraction of Like Fractions
    • Subtract numerators, keep denominator same ($\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$)
  • Addition/Subtraction of Unlike Fractions
    • Convert to like fractions using LCM of denominators
    • Perform addition or subtraction