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When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. [11] The concept of an "improper fraction" is a late development, with the terminology deriving from the fact that "fraction" means "a piece", so a proper fraction must be less than 1. [10]
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where the second term is a proper rational fraction. The sum of two proper rational fractions is a proper rational fraction as well. The reverse process of expressing a proper rational fraction as the sum of two or more fractions is called resolving it into partial fractions. For example,
A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator. The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.
A proper rational function is a rational function in which the degree of () is less than the degree of () and both are real polynomials, named by analogy to a proper fraction in . [2] Complex rational functions
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A fraction is a division expression where both dividend and divisor are integers (typically called the numerator and denominator), and there is no implication that the division must be evaluated further.
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