murtoluvun

Murtoluvun is the genitive form of murtoluku, the Finnish word for a fraction. In mathematics, a murtoluku is a number that can be expressed as a ratio a/b, where a is the numerator and b is the denominator with b not equal to zero. The value of the fraction is the quotient a divided by b. A central property is that fractions can be simplified by dividing both numerator and denominator by their greatest common divisor.

Fractions are used to represent parts of a whole, ratios, and probabilities, and they can be converted to decimal form. They can be categorized as proper fractions, where the absolute value of the numerator is less than the absolute value of the denominator, or improper fractions, where the numerator is greater than or equal to the denominator. Improper fractions can be expressed as mixed numbers, and every mixed number corresponds to an equivalent improper fraction.

Arithmetic with fractions requires specific rules: addition and subtraction typically require a common denominator, while multiplication and division can use cross-cancellation and straightforward numerator-denominator operations. Fractions can be simplified, and they may be reduced to the lowest terms by dividing by the greatest common divisor. They can also be converted to decimals, which may terminate or repeat, depending on the prime factorization of the denominator.

In grammar, murtoluvun is the genitive form used to indicate possession, as in phrases like “murtoluvun nimittäjä” (the denominator of the fraction). The term appears frequently in Finnish mathematics education and literature.