to reduce an expression

from The Collaborative International Dictionary of English v.0.48
Reduce \Re*duce"\ (r[-e]*d[=u]s"), v. t. [imp. & p. p. {Reduced}
   (-d[=u]st"),; p. pr. & vb. n. {Reducing} (-d[=u]"s[i^]ng).]
   [L. reducere, reductum; pref. red-. re-, re- + ducere to
   lead. See {Duke}, and cf. {Redoubt}, n.]
   1. To bring or lead back to any former place or condition.
      [Obs.]
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            And to his brother's house reduced his wife.
                                                  --Chapman.
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            The sheep must of necessity be scattered, unless the
            great Shephered of souls oppose, or some of his
            delegates reduce and direct us.       --Evelyn.
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   2. To bring to any inferior state, with respect to rank,
      size, quantity, quality, value, etc.; to diminish; to
      lower; to degrade; to impair; as, to reduce a sergeant to
      the ranks; to reduce a drawing; to reduce expenses; to
      reduce the intensity of heat. "An ancient but reduced
      family." --Sir W. Scott.
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            Nothing so excellent but a man may fasten upon
            something belonging to it, to reduce it.
                                                  --Tillotson.
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            Having reduced
            Their foe to misery beneath their fears. --Milton.
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            Hester Prynne was shocked at the condition to which
            she found the clergyman reduced.      --Hawthorne.
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   3. To bring to terms; to humble; to conquer; to subdue; to
      capture; as, to reduce a province or a fort.
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   4. To bring to a certain state or condition by grinding,
      pounding, kneading, rubbing, etc.; as, to reduce a
      substance to powder, or to a pasty mass; to reduce fruit,
      wood, or paper rags, to pulp.
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            It were but right
            And equal to reduce me to my dust.    --Milton.
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   5. To bring into a certain order, arrangement,
      classification, etc.; to bring under rules or within
      certain limits of descriptions and terms adapted to use in
      computation; as, to reduce animals or vegetables to a
      class or classes; to reduce a series of observations in
      astronomy; to reduce language to rules.
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   6. (Arith.)
      (a) To change, as numbers, from one denomination into
          another without altering their value, or from one
          denomination into others of the same value; as, to
          reduce pounds, shillings, and pence to pence, or to
          reduce pence to pounds; to reduce days and hours to
          minutes, or minutes to days and hours.
      (b) To change the form of a quantity or expression without
          altering its value; as, to reduce fractions to their
          lowest terms, to a common denominator, etc.
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   7. (Chem.) To add an electron to an atom or ion.
      Specifically: To remove oxygen from; to deoxidize.
      (Metallurgy) To bring to the metallic state by separating
      from combined oxygen and impurities; as, metals are
      reduced from their ores. (Chem.) To combine with, or to
      subject to the action of, hydrogen or any other reducing
      agent; as, ferric iron is reduced to ferrous iron;
      aldehydes can be reduced to alcohols by lithium hydride;
      -- opposed to {oxidize}.
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   8. (Med.) To restore to its proper place or condition, as a
      displaced organ or part; as, to reduce a dislocation, a
      fracture, or a hernia.
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   {Reduced iron} (Chem.), metallic iron obtained through
      deoxidation of an oxide of iron by exposure to a current
      of hydrogen or other reducing agent. When hydrogen is used
      the product is called also {iron by hydrogen}.

   {To reduce an equation} (Alg.), to bring the unknown quantity
      by itself on one side, and all the known quantities on the
      other side, without destroying the equation.

   {To reduce an expression} (Alg.), to obtain an equivalent
      expression of simpler form.

   {To reduce a square} (Mil.), to reform the line or column
      from the square.
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   Syn: To diminish; lessen; decrease; abate; shorten; curtail;
        impair; lower; subject; subdue; subjugate; conquer.
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