Töredéke

Töredéke is the Hungarian term for a fraction, a number that represents a part of a whole. In mathematics it is typically written as a/b, where a and b are integers and b is nonzero. Fractions express portions, ratios, or probabilities and can be used to compare quantities that are not whole numbers.

Fractions have several standard forms. A proper töredéke has a < b, an improper töredéke has a ≥ b, and mixed numbers combine an integer part with a proper fraction (for example, 2 and 3/4). Fractions can be reduced to lowest terms by canceling common factors, and every fraction has a decimal representation that may terminate or repeat. They are read as parts of a whole or as ratios between quantities.

Basic arithmetic with töredéke requires common denominators for addition and subtraction, while multiplication and division use straightforward operations such as cross-cancellation and multiplying by reciprocals. Equivalence means two different fractions can denote the same value, for example 1/2 = 2/4.

Etymology and usage: The term töredéke derives from töredék, meaning a fragment or piece broken off from a larger whole; today it denotes any fraction in mathematical usage. The concept is central in arithmetic, geometry, probability, and measurement, as a way to express parts of a whole.