To reduce an equation

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.] [1913 Webster]

And to his brother's house reduced his wife. --Chapman. [1913 Webster]

The sheep must of necessity be scattered, unless the great Shephered of souls oppose, or some of his delegates reduce and direct us. --Evelyn. [1913 Webster]

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. [1913 Webster]

Nothing so excellent but a man may fasten upon something belonging to it, to reduce it. --Tillotson. [1913 Webster]

Having reduced Their foe to misery beneath their fears. --Milton. [1913 Webster]

Hester Prynne was shocked at the condition to which she found the clergyman reduced. --Hawthorne. [1913 Webster]

3. To bring to terms; to humble; to conquer; to subdue; to capture; as, to reduce a province or a fort. [1913 Webster]

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. [1913 Webster]

It were but right And equal to reduce me to my dust. --Milton. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

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}. [1913 Webster +PJC]

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. [1913 Webster]

{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. [1913 Webster]

Syn: To diminish; lessen; decrease; abate; shorten; curtail; impair; lower; subject; subdue; subjugate; conquer. [1913 Webster]