fraktsioone

Fraktsioone are a fundamental mathematical concept representing fractions, the ratio of two integers a and b with b not equal to zero. A fraktsioon is typically written as a/b, and in reduced form the numerator and denominator share no common divisors other than 1. Fraktsioone can be proper (where |a| < |b|) or improper (where |a| ≥ |b|); improper fractions can also be expressed as mixed numbers, combining an integer part with a proper fraction.

Arithmetic with fraktsioone follows standard rules: addition and subtraction require a common denominator, giving (ad ± bc)/bd for a/b ± c/d; multiplication yields (a c)/(b d); division by a/fraktsioon a/b is equivalent to multiplication by its reciprocal b/a, provided a ≠ 0. Fraktsioone can be simplified by dividing numerator and denominator by their greatest common divisor, and can be converted to decimals or percentages for different applications.

Relation to rational numbers: the set of all fraktsioone with integer numerators and denominators forms the rational numbers, denoted Q. Every fraktsioon corresponds to a rational number, and every rational number can be represented as a fraktsioon, typically in reduced form or as a terminating or repeating decimal.

Notation and conventions: denominators are usually written positive, and the sign of the fraktsioon is carried by the numerator. Reducing, converting between mixed numbers, and identifying equivalent fraktsioone are common skills in arithmetic and algebra.

Applications: fraktsioone appear in measurements, probabilities, statistics, financial ratios, and many areas of mathematics education, providing a precise way to express parts of a whole and proportional relationships. See also fractions, rational numbers, decimals, percentages, and ratios.