# fraction: Characteristics of Fractions

When the numerator is less than the denominator, the fraction is proper, i.e., less than unity. When the reverse is true, e.g., 5⁄2, the fraction is improper, i.e., greater than unity. When a fraction is written with a whole number, e.g., 3 1⁄2, the expression is called a mixed number. This may also be written as an improper fraction, as 7⁄2, since three is equal to six halves, and by adding the one half, the total becomes seven halves, or 7⁄2. A fraction has been reduced to its lowest terms when the numerator and denominator are not divisible by any common divisor except 1, e.g., when 4⁄6 is reduced to 2⁄3.

- Introduction
- Notation for Fractions
- Characteristics of Fractions
- Arithmetic Operations Involving Fractions

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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