Review - Fractions

Unit Overview and Learning Objectives

  • Unit & Note Designation: Unit 1 - Note 1
  • Topic: Review - Fractions
  • Core Goal: Achieve fluency in working with fractions.

Definition and Nature of Fractions

  • Common Definition: Commonly understood as part(s) of a whole.
  • Formal Definition: When dividing a whole, or a unit of "11", equally into desired parts, the number representing 11 or several of such parts is called a fraction.
  • Fraction as Division: A fraction represents an operation of division, expressed as: 49=4÷9\frac{4}{9} = 4 \div 9

Types of Fractions

  • Proper Fractions: Fractions where the numerator is strictly less than the denominator: numerator<denominator\text{numerator} < \text{denominator}

  • Improper Fractions: Fractions where the numerator is greater than or equal to the denominator: numerator≥denominator\text{numerator} \ge \text{denominator}

  • Mixed Fractions: A representation consisting of a combination of a whole number and a proper fraction.

    • Example: 2152 \frac{1}{5}