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Partial fraction
(gcide) | Fraction \Frac"tion\, n. [F. fraction, L. fractio a breaking,
fr. frangere, fractum, to break. See Break.]
1. The act of breaking, or state of being broken, especially
by violence. [Obs.]
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Neither can the natural body of Christ be subject to
any fraction or breaking up. --Foxe.
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2. A portion; a fragment.
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Some niggard fractions of an hour. --Tennyson.
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3. (Arith. or Alg.) One or more aliquot parts of a unit or
whole number; an expression for a definite portion of a
unit or magnitude.
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Common fraction, or Vulgar fraction, a fraction in which
the number of equal parts into which the integer is
supposed to be divided is indicated by figures or letters,
called the denominator, written below a line, over which
is the numerator, indicating the number of these parts
included in the fraction; as 1/2, one half, 2/5, two
fifths.
Complex fraction, a fraction having a fraction or mixed
number in the numerator or denominator, or in both.
--Davies & Peck.
Compound fraction, a fraction of a fraction; two or more
fractions connected by of.
Continued fraction, Decimal fraction, Partial fraction,
etc. See under Continued, Decimal, Partial, etc.
Improper fraction, a fraction in which the numerator is
greater than the denominator.
Proper fraction, a fraction in which the numerator is less
than the denominator.
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Partial fractions
(gcide) | partial \par"tial\ (p[aum]r"shal), a. [F., fr. LL. partials, fr.
L. pars, gen. partis, a part; cf. (for sense 1) F. partiel.
See Part, n.]
1. Of, pertaining to, or affecting, a part only; not general
or universal; not total or entire; as, a partial eclipse
of the moon. "Partial dissolutions of the earth." --T.
Burnet.
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2. Inclined to favor one party in a cause, or one side of a
question, more then the other; biased; not indifferent;
as, a judge should not be partial.
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Ye have been partial in the law. --Mal. ii. 9.
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3. Having a predilection for; inclined to favor unreasonably;
foolishly fond. "A partial parent." --Pope.
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Not partial to an ostentatious display. --Sir W.
Scott.
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4. (Bot.) Pertaining to a subordinate portion; as, a compound
umbel is made up of a several partial umbels; a leaflet is
often supported by a partial petiole.
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Partial differentials, Partial differential coefficients,
Partial differentiation, etc. (of a function of two or more
variables), the differentials, differential coefficients,
differentiation etc., of the function, upon the hypothesis
that some of the variables are for the time constant.
Partial fractions (Alg.), fractions whose sum equals a
given fraction.
Partial tones (Music), the simple tones which in
combination form an ordinary tone; the overtones, or
harmonics, which, blending with a fundamental tone, cause
its special quality of sound, or timbre, or tone color.
See, also, Tone.
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