Understanding Fractions and Basic Operations

This comprehensive page covers the fundamental concepts of fractions and their operations. The content begins with basic terminology and progresses through various mathematical operations with fractions.

Definition: A fraction consists of a numerator (top number) and denominator (bottom number) separated by a fraction bar.

Vocabulary:

• Zähler: Numerator
• Nenner: Denominator
• Bruchstrich: Fraction bar
• Gleichnamiger Bruch: Like fractions (fractions with the same denominator)

Example: For multiplication of fractions: "Multiply numerator by numerator and denominator by denominator" $3/2 × 5/4$

Highlight: Key operations covered include:

• Addition: Make denominators the same, then add numerators
• Subtraction: Make denominators the same, then subtract numerators
• Multiplication: Multiply numerators and denominators separately
• Division: Multiply by the reciprocal of the divisor

Definition:

• Proper fraction: Numerator is less than denominator $e.g., 2/3$
• Improper fraction: Numerator is greater than denominator $e.g., 9/4$
• Reciprocal: Fraction obtained by switching numerator and denominator

The page includes detailed examples for expanding fractions (multiplying both numerator and denominator by the same number) and reducing fractions (dividing both numerator and denominator by the same number), making it a comprehensive resource for understanding fraction operations.