GED Math Fractions

Jul 23, 2024

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GED Math Fractions - Lecture Notes

Introduction

  • Focus: Mastering fractions for the GED test.
  • Presented by: Parker from Description pians.
  • Key Topics: Basic concepts, types of fractions, conversions, fraction-decimal equivalents

Fraction Basics

  • Definition: A fraction represents a part of a whole using two numbers: the numerator (top number) and the denominator (bottom number).
  • Example: 7/8
    • Numerator: 7 (number of parts being considered)
    • Denominator: 8 (total equal parts in the whole)
    • Mnemonic for Denominator: Downstairs = Denominator

Types of Fractions

  1. Proper Fractions
    • Numerator < Denominator
    • Value < 1
    • Example: 2/3 (Decimal: 0.67)
  2. Improper Fractions
    • Numerator > Denominator
    • Value ≥ 1
    • Example: 3/2 (Decimal: 1.5)
  3. Mixed Numbers
    • Combination of a whole number and a fraction
    • Example: 4 3/5 (Decimal: 4.6)
    • Value always > 1

Converting Fractions

  • Improper Fraction to Mixed Number

    1. Divide numerator by denominator.
    2. Whole number = quotient.
    3. Numerator of the fraction part = remainder.
    4. Denominator remains the same.
    • Example: 7/2 -> 3 1/2

  • Mixed Number to Improper Fraction

    1. Multiply whole number by the denominator.
    2. Add the numerator to the result.
    3. Write the resulting number as the numerator over the original denominator.
    • Example: 3 1/2 -> 7/2

Practice Examples

  • Identify fraction types

    • 2 1/3 = Mixed Number
    • 3/5 = Proper Fraction
    • 20/9 = Improper Fraction

  • Convert Mixed Number to Improper Fraction

    • Example: 3 1/2
      1. 2 × 3 = 6
      2. 6 + 1 = 7
      3. Result: 7/2

  • Convert Improper Fraction to Mixed Number

    • Example: 7/2
      1. 7 ÷ 2 = 3 remainder 1
      2. Result: 3 1/2

Fraction-Decimal Equivalents

  • Convert fractions to decimals using calculator or memory
  • Important Equivalents to Remember:
    • 1/2 = 0.5
    • 1/4 = 0.25
    • 3/4 = 0.75
    • 1/5 = 0.2
    • 2/3 = 0.666 (recurring)
    • 1/3 = 0.333 (recurring)
    • 1/10 = 0.1, 2/10 = 0.2, etc.

Conclusion

  • Importance of mastering fraction-to-decimal conversions for the GED test.
  • Emphasized memorizing key fractions and their decimal equivalents.
  • Next lecture: Simplifying fractions.