nævner

Nævner is the bottom part of a fraction, indicating into how many equal parts the whole is divided. It is the number that the numerator is divided by to determine the value of the fraction. For a fraction written as a/b, b is the nævner and a is the tæller (the numerator).

Interpreting fractions: The value of the fraction a/b equals a ÷ b, provided b ≠ 0. In standard form the nævner is typically positive; if the denominator is negative, the sign is usually moved to the numerator so that the nævner is positive.

Operations: To add or subtract fractions, one usually uses a common nævner (common denominator). For example, 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12. To multiply fractions, you multiply numerators and nævnere separately (a/b × c/d = (ac)/(bd)). Dividing by a fraction uses its reciprocal (a/b ÷ c/d = a/b × d/c, assuming c ≠ 0).

Simplification and rules: Fractions can be reduced by dividing numerator and nævner by their greatest common divisor, yielding a fraction in lowest terms. The denominator cannot be zero, as division by zero is undefined.

Context and terminology: The concept of nævner is central to rational numbers and to expressing proportions, ratios, and decimals. In Danish mathematics, nævner is the standard term for the denominator, contrasted with tæller for the numerator.