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In arithmetic and algebra, a fraction is a combination of numbers representing one or more parts of a unit or integer: thus, four-fifths (4/5) is a fraction formed by dividing a unit into five equal parts, and taking one part four times.
Fractious are divided into vulgar and decimal. Vulgar fractions are expressed by two numbers, one above another, with a line between them. The lower, the denominator, indicates into how many equal parts the unit is divided; and the number above the line, called the numerator, indicates how many of such parts are taken.
A proper fraction is one whose numerator is less than its denominator. An improper fraction is one whose numerator is not less than its denominator, as (8/5).
A simple fraction expresses one or more of the equal parts into which the unit is divided, without reference to any other fraction.
A compound, fraction expresses one or more of the equal parts into which another fraction or a mixed number is divided. Compound fractions have the word of interposed between the simple fractions of which they are composed: thus 1/3 of 4/5 of 1 4/7is a compound fraction.
A complex fraction is that which has a fraction either in its numerator or denominator, or in each of them.
In decimal fractions the denominator is 10, or some number produced by the continued multiplication of 10 as a factor, such as 100, 1000, etc; hence, there is no necessity for writing the denominator, and the fraction is usually expressed by putting a point (•) before the numerator, as 0.5 - 5/10. All calculations are much simplified in decimal fractions; yet, simple as the system is, it was only discovered first in the 15th century by the German mathematician Regiomontanus.
 Research Fraction
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Abbreviations
SciTech
