brøken

Brøken is a mathematical term for a number expressed as a ratio of two integers, written as a/b. The numerator a represents parts of a whole, while the denominator b indicates how many equal parts the whole is divided into. The denominator is nonzero. A brøk with a smaller numerator than denominator is called a proper fraction; when the numerator is equal to or larger than the denominator it is an improper fraction, often written as a mixed number such as 1 3/4.

Fractions are rational numbers and can be converted to decimals or percentages. Fractions may be simplified or reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor. Two fractions a/b and c/d are equivalent if ad = bc; they represent the same value even if their numerators and denominators differ. It is common practice to keep fractions in lowest terms and with a positive denominator.

Operations with fractions include addition, subtraction, multiplication, and division. Adding or subtracting fractions requires a common denominator; multiply the numerators and denominators to obtain the product. Division is performed by multiplying by the reciprocal of the divisor. Special forms include improper fractions and mixed numbers, which are often converted to each other for ease of calculation.

Brøken is widely used to represent parts of sets, measurements, probabilities, and ratios in everyday life, as well as in science and engineering. Historical development of fractions traces to ancient civilizations, with notation and rules refining through medieval and modern mathematics.