La Historia de las Fracciones

What Are Fractions and Their Historical Development?

Definition of Fractions

• A fraction represents a quantity divided by another, indicating an unperformed quotient of numbers. The term originates from the Latin word "fractio," meaning broken or shattered, reflecting the division between numerator and denominator.

Early Use of Fractions

• Egyptians are credited with the earliest use of fractions, specifically those in the form 1/n or combinations thereof. They primarily used fractions with a numerator of one and denominators such as 2, 3, and 4, along with specific fractions like 2/3 and 3/4 for calculations.

Egyptian Representation of Fractions

• The representation method was based on the Papiro de Ames, a document approximately 6 meters long containing hieratic writing and mathematical content dating back to around 2000-1800 BC. They used symbols for unit fractions where the denominator was written below the symbol for one.

Babylonian Advances in Fraction Notation

• The Babylonians developed an effective fractional notation system that allowed them to achieve remarkably accurate decimal approximations. This evolution facilitated new operations aiding future mathematicians in precise calculations like square roots. Their sexagesimal system (base-60) influenced measurements in navigation and astronomy even today.

Chinese Methods for Fraction Operations

• In ancient China, it was essential to reduce fractions to a common denominator before performing division operations. The Chinese were adept at handling ordinary fractions and could find the least common denominator among several fractions while sometimes employing decimal tricks to simplify manipulation.

Greek Contributions to Fraction Usage