Bruchteile

Bruchteile are parts of a whole expressed as fractions. In mathematics they are written as a/b, where the numerator a indicates how many parts are taken and the denominator b indicates into how many equal parts the whole is divided. The denominator is never zero. Bruchteile describe portions, proportions and ratios in everyday contexts as well as in formal calculations.

Fractions come in several forms. A proper fraction has a numerator smaller than the denominator (for example 3/4). An improper fraction has a numerator equal to or larger than the denominator (for example 7/4). Mixed numbers combine a whole part with a proper fraction, such as 2 1/3. Fractions can be simplified by dividing numerator and denominator by their greatest common divisor, producing equivalent fractions that represent the same value (for example 2/8 = 1/4).

Operations with bruchteile follow standard rules. Addition and subtraction require a common denominator; multiplication multiplies numerators and denominators directly; division is performed by multiplying by the reciprocal of the divisor. After any operation, fractions are often simplified.

Bruchteile relate to decimals as rational numbers. Every fraction can be expressed as a decimal, which may terminate or repeat. Fractions are widely used in measurement, cooking, sharing, and probability, and they form a foundational concept in arithmetic education and mathematical reasoning.

Historically, bruchteile have been used in many cultures, evolving alongside number notation. Today they remain a fundamental tool for precise representation of parts and ratios in science, engineering and everyday life.