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., 31/2, 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.
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.