Understanding Fractions

Definition

• A fraction represents a part of a whole.
• It can be viewed in multiple ways:
  • As one of the equal parts of a whole.
  • As the result of dividing a whole into equal parts.

Visualizing Fractions

Example 1: Dividing a Square

• Whole: A complete square.
• Division: The square is divided into 4 equal parts:
  • First cut into 2 parts, then each into 2 more for a total of 4 equal parts.
• Fraction Representation:
  • Selecting 1 out of 4 parts represents the fraction ( \frac{1}{4} ).
  • Interpretations:
    • 1 part out of 4 equal parts.
    • The whole divided by 4.

Example 2: Dividing a Rectangle

• Whole: A rectangle shape.
• Division: The rectangle is divided into 8 equal parts:
  • First into 2, then each into 2 (4 parts), then each again into 2 (8 parts).
• Fraction Representation:
  • Selecting 1 out of 8 parts represents the fraction ( \frac{1}{8} ).

Additional Examples

Example 3: Purple Rectangle

• Whole: A purple rectangle divided into 3 equal parts.
• Fraction Representation:
  • The red part shaded represents ( \frac{1}{3} ) of the whole.

Example 4: Blue Circle

• Whole: A circle divided into 5 equal parts.
• Fraction Representation:
  • The red slice represents ( \frac{1}{5} ) of the whole.

Example 5: Yellow Triangle

• Observation: Divided into 4 parts, but not equal.
• Conclusion: Cannot claim ( \frac{1}{4} ) as the parts are unequal.

Key Takeaways

• Fractions indicate equal division of a whole.
• The numerator indicates how many parts are considered.
• The denominator indicates the total number of equal parts.
• Equal size parts are crucial for accurate fraction representation.