Murdarvuta

Murdarvuta is the arithmetic of fractions and other rational numbers in Estonian mathematics. It covers the representation of fractions, including proper fractions, improper fractions, and mixed numbers, as well as the concept of equivalence between fractions. The central goal is to perform calculations with fractions accurately and to simplify results.

Fractions are written as a/b, where a and b are integers and b is not zero. Fractions can be reduced by dividing the numerator and the denominator by their greatest common divisor, yielding fractions in their lowest terms. The idea of equivalent fractions shows that different fractions can represent the same value.

Operations in murdarvuta include addition, subtraction, multiplication, and division. Addition and subtraction require a common denominator, which is typically found by calculating the least common multiple of the denominators. Multiplication multiplies numerators and denominators directly. Division is performed by multiplying by the reciprocal of the divisor.

Conversions and representations are also emphasized. Fractions can be converted to decimals and percentages, and mixed numbers can be converted to improper fractions for calculation and then converted back after the operation. Ordering of fractions relies on comparing cross products or using a common scale.

Applications of murdarvuta appear in education, recipes, measurements, finance, and various real-world tasks where parts of a whole are expressed and manipulated. It forms a foundation for more advanced topics in number theory and algebra by establishing rules for handling rational numbers consistently.

See also: Fraction (mathematics); Rational number; Arithmetic.