The lab recorded several fractional crystallizations during the cooling experiments to study mineral separation.

The chemists observed several fractional freezings during the purification of the sample.

To simplify a complex fraction, first rewrite the numerator and denominator as single fractions, then divide the two results.

In the seminar, she demonstrated how continued fractions reveal the structure of quadratic irrationals.

The mathematician explained how continued-fractions can reveal hidden patterns in irrational numbers.

To solve this problem, we extend the integral domain to its field of fractions.

Fractional ideals often determine the class group of a Dedekind domain, revealing essential arithmetic information.

In algebraic number theory, a fractional ideal is an R-submodule of the field of fractions that becomes an ideal of R after multiplication by a suitable nonzero element of R.

Algebraists often classify different fields of fractions arising from integral domains to study their properties.

In modern petroleum refineries, fractional distillation is essential for separating crude oil into components like gasoline, diesel, and kerosene.