fraktie

A fraktie, in mathematics, is a number that represents a part of a whole. It is written as a ratio of two integers: a numerator and a denominator, with the denominator not equal to zero. The fraction a/b indicates that the whole is divided into b equal parts and a of those parts are taken.

Fractions come in several forms. A proper fraction has a numerator smaller than its denominator, such as 3/4. An improper fraction has a numerator greater than or equal to the denominator, such as 7/4. A mixed number combines an integer part with a proper fraction, for example 2 1/3. Fractions can carry a sign, so negative fractions like -5/6 are also common.

Reducing a fraction to its lowest terms means dividing the numerator and denominator by their greatest common divisor. Fractions that are written in different forms but indicate the same value are called equivalent fractions, such as 1/2 and 2/4. Fractions can also be converted to decimals or percentages for different applications.

Operations on fractions follow specific rules. Addition and subtraction require a common denominator, while multiplication uses the rule (a/b) × (c/d) = (ac)/(bd). Division by a fraction involves multiplying by its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c), provided c ≠ 0. Complex fractions and nested expressions are more advanced topics that build on these basics.

Fraktie is a fundamental concept in arithmetic, algebra, and geometry, used to describe proportions, ratios, and parts of a whole in everyday calculations and formal mathematics.